% Here are the references found by using the search command

find_out '/nterpolat/&&(/[Bb]ivariate/||/[Mm]ultivariate/||/ergin/||/akopian/)'

% to find the references in the data base maintained by Carl de Boor that 
% involve the word 'interpolation' together with any of 'bivariate', 
% 'multivariate', 'Kergin', or 'Hakopian'

% for additional details about this data base write to 
% deboor@cs.wisc.edu or waldron@math.wisc.edu
% or visit    http://www.cs.wisc.edu/~deboor/bib/bib.html 

%AbouirCuyt93
% carl
\refJ Abouir, J., Cuyt, A.;
Multivariate partial Newton-Pad\'e and Newton-Pad\'e type approximants;
\JAT; 72; 1993; 301--316;
% multivariate polynomial interpolation

%Ahlin64
% carl
\refJ Ahlin, A. C.;
A bivariate generalization of Hermite's interpolation formula;
\MC; 18(86); 1964; 264--273;

%Akima74
\refJ Akima,  H.;
Bivariate interpolation and smooth surface fitting based on local
 procedures;
\CACM; 17; 1974; 26--31;

%Akima74b
\refJ Akima,  H.;
A method of bivariate interpolation and smooth surface fitting based
on local procedures;
\CACM; 17; 1974; 18--20;

%Akima78
\refJ Akima,  H.;
Algorithm 526: bivariate interpolation and smooth fitting for
irregularly distributed data points;
\ACMTMS; 4; 1978; 160--164;

%Akima78b
\refJ Akima,  H.;
A method of bivariate interpolation and smooth surface fitting
 for irregularly distributed data points;
\ACMTMS; 4; 1978; 144--159;

%Akima84b
% larry
\refJ Akima,  H.;
On estimating partial derivatives for bivariate interpolation of scattered
data;
\RMJM; 14; 1984; 41--52;

%Alfeld85a
% peter
\refJ Alfeld,  P.;
Multivariate perpendicular interpolation;
\SJNA; 22; 1985; 95--106;

%ArcangeliGout76
% carl
\refJ Arcangeli,  R., Gout, J. L.;
Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de
$\RR^n$;
\RAIROAN; 10(3); 1976; 5--27;
% multivariate, interpolation, error, polynomial

%Bamberger85
% larry
\refP Bamberger,  L.;
Interpolation in bivariate spline spaces;
\MvatIII; 25--34;

%BarnhillGregory75a
% larry, carl
\refJ Barnhill, R. E., Gregory, J. A.;
Polynomial interpolation to boundary data on triangles;
\MC; 29(131); 1975; 726--735;
% bivariate interpolation, Coons patches for triangles, polynomial blending
% functions, blending functions, interpolation methods, Boolean sum
% interpolation, curved boundery finite elements.

%BarnhillWhiteman73
% carl
\refP Barnhill,  R. E., Whiteman, J. R.;
Error analysis of finite element methods with triangles for elliptic
boundary value problems;
\BrunelI; 83--112;
% numerical quadrature, interpolation, multivariate

%BarnhillWixom69
% larry
\refJ Barnhill,  R. E., Wixom, J. A.;
An error analysis for the bivariate interpolation of analytic functions;
\SJNA; 6; 1969; 450--457;

%BaszenskiDelvos86
\refR Baszenski,  G., Delvos, F.-J.;
Boolean algebra and multivariate interpolation;
Bochum; 1986;

%BaszenskiDelvosPosdorf79
\refP Baszenski,  G., Delvos, F. J., Posdorf, H.;
Boolean methods in bivariate reduced Hermite interpolation;
\MvatI; 47--58;

%BaszenskiDelvosPosdorf80b
% larry
\refP Baszenski,  G., Delvos, F. J., Posdorf, H.;
Representation formulas for conforming bivariate interpolation;
\TexasIII; 193--198;

%BazeleyCheungIronsZienkiewicz66
% .
\refQ Bazeley,  G. P., Cheung, Y. K., Irons, B. M., Zienkiewicz, O. C.;
Triangular elements in plate bending, conforming and nonconforming solutions;
(Proc.\ 1st Conf.\ Matrix Methods in Structure Mechanics, AFFDL-TR-CC--80), 
xxx (ed.), Wright Patterson A.F. Base (Ohio); 1966; 547--576;
% nonconforming, FEM, multivariate, polynomial interpolation

%BenOrTiwary88
\refJ Ben-Or,  ?., Tiwari, Prasoon;
A deterministic algorithm for sparse multivariate polynomial interpolation;
STOC-88; {}; 1988; 301--309;

%BinevJetter92b
% sherm
\refP Binev,  P. G., Jetter, K.;
Estimating the condition number for multivariate interpolation problems;
\Nmatnion; 39--50;

%Birkhoff79
% carl
\refQ Birkhoff,  G.;
The algebra of multivariate interpolation;
(Constructive approaches to mathematical models), C. V. Coffman and G. J.
Fix (eds.), Academic Press (New York); 1979; 345--363;

%BlagaComan81
\refJ Blaga,  P., Coman, G.;
Multivariate interpolation formulas of Birkhoff type;
Studia Univ.\ Babes-Bolyai, Ser.\ Math.; XX;  1981; 14--22;

%BojanovHakopianSahakian93
% .
\refB Bojanov,  B. D., Hakopian, H. A., Sahakian, A. A.;
Spline Functions and Multivariate Interpolations;
Kluwer Academic Publishers (Dordrecht, The Netherlands); 1993;
% ISBN 0-7923-2229-0

%Boor92
% carl
\refJ Boor,  C. de;
On the error in multivariate polynomial interpolation;
Applied Numerical Mathematics; 10; 1992; 297--305;

%BoorHolligRiemenschneider83
% larry
\refP Boor,  C. de, H\"ollig, K., Riemenschneider, S.;
Bivariate cardinal interpolation;
\TexasIV; 359--363;

%BoorHolligRiemenschneider84
\refP Boor,  C. de, H\"ollig, K., Riemenschneider, S. D.;
On bivariate cardinal interpolation;
\VarnaI; 
254--259;

%BoorHolligRiemenschneider85b
% carl
\refJ Boor,  C. de, H\"ollig, K., Riemenschneider, S.;
Bivariate cardinal interpolation by splines
  on a three-direction mesh;
\IJM; 29; 1985; 533--566;

%BoorHolligRiemenschneider85c
% carl
\refJ Boor,  C. de, H\"ollig, K., Riemenschneider, S.;
Convergence of bivariate cardinal interpolation;
\CA; 1; 1985; 183--193;

%BoorHolligRiemenschneider85d
\refP Boor,  C. de, H\"ollig, K., Riemenschneider, S. D.;
On bivariate cardinal interpolation;
\VarnaI; 
254--259;

%BoorRon90
% greg
\refJ Boor,  C. de, Ron, A.;
On multivariate polynomial interpolation;
\CA; 6; 1990; 287--302;

%Bos83
% sonya
\refJ Bos,  L.;
On Kergin interpolation in the disk;
\JAT; 37; 1983; 251--261;

%Buhmann90a
% greg
\refJ Buhmann,  M. D.;
Multivariate interpolation in odd-dimensional Euclidean spaces using 
multiquadrics;
\CA; 6; 1990; 21--34;

%Buhmann90b
% greg
\refJ Buhmann,  M. D.;
Multivariate cardinal interpolation with radial-basis functions;
\CA; 6; 1990; 225--255;

%CarlsonR82
\refJ Carlson,  R. E.;
A bivariate interpolation algorithm for scattered data;
\RMJM; xx; xx; xx;

%CarlsonRFritsch91
% larry
\refJ Carlson,  R. E., Fritsch, F. N.;
A bivariate interpolation algorithm for data which are monotone in one
variable;
\SJSSC; 12; 1991; 859--866;

%CavarettaGoodmanMicchelliSharma83
% sherm, proper Proceedings reference
\refP Cavaretta,  A. S., Goodman, T. N. T., Micchelli, C. A., Sharma, A.;
Multivariate interpolation and the Radon transform: III. Lagrange
representation;
\EdmontonII; 37--50;

%CavarettaMicchelliSharma80
% larry
\refJ Cavaretta,  A. S., Micchelli, C. A., Sharma, A.;
Multivariate interpolation and the Radon transform;
\MZ; 174; 1980; 263--279;

%CavarettaMicchelliSharma80a
\refP Cavaretta,  A. S., Micchelli, C. A., Sharma, A.;
Multivariate interpolation and the Radon transform: II. Some further
examples;
\BonnII; 49--61;

%CavarettaMicchelliSharma83
% .
\refJ Cavaretta,  A. S., Micchelli, C. A., Sharma, A.;
Multivariate interpolation and the Radon transform.\ Part III
Lagrange representation;
Can.\ Math.\ Soc.\ Conf.\ Proc.; 3; 1983; 37--50;

%ChuiDiamond87
\refJ Chui,  C. K., Diamond, H.;
A natural formulation of quasi-interpolation by multivariate splines;
\PAMS; 99; 1987; 643--646;

%ChuiDiamond90
% carl
\refJ Chui,  Charles K., Diamond, Harvey;
A characterization of multivariate quasi-interpolation formulas and its
applications;
\NM; 57; 1990; 105--121;

%ChuiDiamondRaphael88b
% carl
\refJ Chui, Charles K., Diamond, Harvey, Raphael, Louise A.;
Interpolation by multivariate splines;
\MC; 51(183); 1988; 203--218;
% optimal order, box splines, fundamental function, numerical implimentation.

%ChuiDiamondRaphael99
\refJ Chui,  C. K., Diamond, H., Raphael, L. A.;
Interpolation by bivariate quadratic splines on nonuniform rectangles;
Trans.\ Fourth Army Conf.\ Appl.\ Math.\ Comp; XX; XX; XX;

%ChuiHe87
% larry
\refP Chui,  C. K., He, Tian-Xiao;
On the location of sample points in $C^1$ quadratic bivariate spline 
interpolation;
\NmatVIII; 30--42;

%ChuiHe90a
% larry, carl
\refJ Chui, Charles K., He, Tian-Xiao;
Bivariate $C^1$ quadratic finite elements and vertex splines;
\MC; 54(189); 1990; 169--187;
% interpolation, quasi-interpolation, macroelements.

%ChuiHeWang86
% author
\refP Chui,  C. K., He, Tian-Xiao, Wang, Ren-Hong;
Interpolation by bivariate linear splines;
\Szabados; 247--255;

%ChuiJetterWard87
% carl
\refJ Chui, Charles K., Jetter, K., Ward, J. D.;
Cardinal interpolation by multivariate splines;
\MC; 48(178); 1987; 711--724;
% scaled cardinal interpolation, Fourier transform, discrete Fourier
% transform, box splines, Marsden identity.

%ChuiLai87a
% greg
\refJ Chui,  C. K., Lai, M.-J.;
A multivariate analog of Marsden's identity and a
	 quasi-interpolation scheme;
\CA; 3; 1987; 111--122;

%ChuiStocklerWard89a
\refR Chui,  C. K., St\"ockler, J., Ward, J. D.;
Bivariate cardinal interpolation with a shifted box-spline on a 
three-directional mesh;
CAT Report 188, Texas A\&M University; 1989;

%CiarletWagschal71
% carl
\refJ Ciarlet,  P., Wagschal, C.;
xxx;
\NM; 17; 1971; 84--100;
% interpolation, multivariate

%CostantiniFontanella90
% larry
\refJ Costantini,  P., Fontanella, F.;
Shape preserving bivariate interpolation;
\SJNA; 27; 1990; 488--506;

%Daehlen87
% greg
\refJ D{\ae}hlen,  M.;
An example of bivariate interpolation with translates of 
$C^0$-quadratic box-splines on a three direction mesh;
\CAGD; 4; 1987; 251--255;

%DaehlenLyche88
% carl
\refJ D{\ae}hlen, Morten, Lyche, Tom;
Bivariate interpolation with quadratic box splines;
\MC; 51(183); 1988; 219--230;
% three-direction grid.

%Delvos79b
\refJ Delvos,  F. J.;
Boolean bivariate Lagrange interpolation;
Computing; 22; 1979; 311--323;

%Delvos84
% needs check
\refP Delvos,  F. J.;
On bivariate Hermite trigonometric interpolation;
\VarnaI;  266--272;

%DelvosKosters75
% larry
\refJ Delvos,  F. J., K\"osters, H. W.;
On the variational characterization of
	 bivariate interpolation methods;
\MZ; 145; 1975; 129--137;

%DelvosPosdorf80
\refJ Delvos,  F. J., Posdorf, H.;
A Boolean method in bivariate interpolation;
Anal.\ Numer.\ Th.\ Approx.; 9; 1980; 35--45;

%DelvosPosdorfSchempp78
% sherm, Proceedings update
\refP Delvos,  F. J., Posdorf, H., Schempp, W.;
Serendipity type bivariate interpolation;
\HandscombII; 47--56;

%Dimitrov91
\refR Dimitrov,  D. K.;
Hermite interpolation by bivariate continuous super splines;
Bulgarian Acad.\ of Sciences; xxx;

%DoddMcAllisterRoulier83
% carl
\refJ Dodd, S. L., McAllister, David F., Roulier, John A.;
Shape-preserving spline interpolation for specifying bivariate
 functions on grids;
\ICGA; 3(7); 1983; 70--79;

%DynRon90a
\refP Dyn,  N., Ron, A.;
On multivariate polynomial interpolation;
\ShrivenhamII; 177--184;

%DynRon90b
%larry
\refJ Dyn,  N., Ron, A.;
Local approximation by certain spaces of
multivariate exponential-polynomials, approximation order of exponential
box splines and related interpolation problems;
\TAMS; 319; 1990; 381--403;

%EwaldM\"uhligMulanskyxx
\refR Ewald, S., M\"uhlig, H., Mulansky, B.;
Bivariate interpolating and smoothing tensor produce splines;
proceedings 55--68; 19xx;

%Farwig84
\refR Farwig,  R.;
Multivariate interpolation of arbitrarily spaced data by moving least
squares methods;
Rpt.\ 676, Univ.\ Bonn; 1984;

%Farwig86
% larry, carl
\refJ Farwig, Reinhard;
Rate of convergence of Shepard's global interpolation formula;
\MC; 46(174); 1986; 577--590;
% multivariate interpolation.

%Foley79
\refD Foley,  T. A.;
Smooth multivariate interpolation to scattered data;
Arizona State Univ.; 1979;

%Foley83
% larry
\refP Foley,  T. A.;
Full Hermite interpolation to multivariate scattered data;
\TexasIV; 465--470;

%FoleyNielson80
% larry
\refP Foley,  T. A., Nielson, G. M.;
Multivariate interpolation to scattered data using
delta iteration;
\TexasIII; 419--424;

%Franke91
% larry
\refJ Franke,  R.;
Sensitivity of the error in multivariate statistical interpolation to 
parameter values;
Monthly Weather Review; 119; 1991; 815--832;

%Gao88
\refJ Gao,  Junbin;
% .
Multivariate quasi-Newton interpolation;
J. Math.\ Res.\ Exposition;  8(3); 1988; 447--453;

%Gao92
\refR Gao,  J.;
Interpolation and approximation by bivariate splines of 
$S_3^1(\Delta_{mn}^{(1)})$;
Wuhan Univ., China; xxx;

%Gao92a
% carl
\refR Gao,  Junbin;
A remark on multivariate polynomial interpolations;
Research Report No.\ 7, Wuhan University; 1992;
% makes use of BoorRon90 to construct polynomial spaces good for giving
% shape functions for certain nonconforming elements.
% For Zienkiewizc' triangle, gets the least as well as a space involving also
% some quartic polynomials.\ No proofs or arguments as why these are good 
% choices.

%Gao93
% carl
\refR Gao,  Junbin;
Interpolation methods for the construction of shape function space of
nonconforming finite elements;
preprint, Huazhong U. of Science and Technology (Wuhan, PRC); 1993;
% nonconforming, FEM, multivariate, polynomial interpolation

%Gasca90
% carl
\refP Gasca,  M.;
Multivariate polynomial interpolation;
\Teneriffe; 215--236;

%GascaLopez82
% sonya
\refJ Gasca,  M., Lopez-Carmona, A.;
A general recurrence interpolation formula
and its applications to multivariate interpolation;
\JAT; 34; 1982; 361--374;

%GascaMartinez92
% sherm
\refJ Gasca,  M., Martinez, J. J.;
Bivariate Hermite-Birkhoff interpolation and Vandermonde determinants;
\NA; 3; 1992; 193--199;

%GascaMartinez93a
\refJ Gasca, M., Martinez, J. J.;
Bivariate Hermite-Birkhoff interpolation and Vandermonde determinants;
Numerical Algorithms; 3; 1993; xxx--xxx;

%GascaMuhlbach92
% sherm, update page numbers
\refJ Gasca,  M., M\"uhlbach, G.;
Multivariate polynomial interpolation under projectivities II: Neville-Aitken 
formulas;
\NA; 2; 1992; 255--277;

%GevorgianHakopianSaakyan90a
% carl
\refJ Hakopian,  A. A., Gevorgyan, O. V., Saakyan, A. A.;
On bivariate Hermite interpolation;
Matem.\ Zametki; 48; 1990; 137--139;

%GevorgianHakopianSaakyan92a
% carl
\refJ Hakopiyan,  A. A., Gevorgian, O. V., Saakyan, A. A.;
On bivariate polynomial interpolation (in Russian);
Math.\ Sbornik; 183; 1992; 111--126;

%Gmelig87b
\refQ Gmelig-Meyling,  R. H. J.;
On interpolation by bivariate quintic splines on class $C^2$;
(SPMTb), xxx (ed.), xxx (xxx); 1987; 152--161;

%Gmelig88b
% larry
\refJ Gmelig-Meyling,  R. H. J.;
Smooth interpolation to scattered data by bivariate piecewise polynomials
of odd degree;
\CAGD; 7; 1990; 439--458;

%Gmelig88d
\refP Gmelig-Meyling,  R. H. J. G.;
On interpolation by bivariate quintic splines of class $C^2$;
\VarnaII; 152--161;

%GmeligPfluger90
% greg
\refR Gmelig-Meyling,  R. H. J., Pfluger, P.;
Smooth interpolation to scattered data by bivariate piecewise polynomials
of odd degree;
\CAGD; 7; 1990; 439--458;

%Goodman83b
% sonya
\refJ Goodman,  T. N. T.;
 Interpolation in minimum semi-norm and multivariate B-splines;
\JAT; 37; 1983; 212--223;

%Gordon71d
% larry
\refJ Gordon,  W. J.;
Blending-function methods of bivariate
and multivariate interpolation and approximation;
\SJNA; 8; 1971; 158--177;

%GordonCheney77
\refQ Gordon,  W. J., Cheney, E. W.;
Bivariate and multivariate interpolation
with noncommutative projectors;
(Linear Spaces and Approximation), P. L. Butzer and
B. Sz-Nagy (eds.), Birkh\"auser (Basel); 1977; 381--387;

%GordonWixom78
% larry, carl
\refJ Gordon, William J., Wixom, James A.;
Shepard's method of ``metric
interpolation ''to bivariate and multivariate interpolation;
\MC; 32(141); 1978; 253--264;

%GuanLi89
% carl
\refP Guan,  L\"utai, Li, Yuesheng;
Multivariate polynomial natural spline interpolation to scattered data;
\TexasVI; 311--314;

%Hack87
% sonya
\refJ Hack,  F.;
On bivariate Birkhoff interpolation;
\JAT; 49; 1987; 18--30;

%Hakopian81
% carl
\refJ Hakopian,  H.;
Les diff\'erences dives\'ees de plusieurs variables et les
interpolations multidimensionelles de types lagrangien
et hermitien;
\CRASP; 292; 1981; 453--456;

%Hakopian82
% carl
\refJ Hakopian,  Hakop A.;
Multivariate divided differences and multivariate
interpolation of Lagrange and Hermite type;
\JAT; 34; 1982; 286--305;

%Hakopian82b
% carl
\refJ Hakopian,  Hakop;
Multivariate spline functions, B-spline basis and
polynomial interpolations;
\SJNA; 18; 1982; 510--517;

%Hakopian83a
% carl
\refJ Hakopian,  H.;
On fundamental polynomials of multivariate interpolation I of Lagrange and
Hermite type;
Bull.\ Pol.\ Acad.\ Sci., Math.; 31(3-4); 1983; 137--141;

%Hakopian83b
% carl
\refJ Hakopian,  Hakop;
 Integral remainder formula of the tensor product interpolation;
Bull.\ Pol.\ Acad.\ Sci., Math.; 31(5-8); 1983; 267--272;
% interpolation from \Pi_\Gamma at the \Gamma subset of a rectangular
% grid is correct in case \Gamma is a shadow set (or, left set).

%Hakopian83c
% author
\refQ Hakopian,  H.;
Duality of multivariate polynomial interpolation (in Russian);
(Internat.\ Conf.\ Approx.\ Theory), xxx (ed.), (Kiev); 1983; 8--10;
% The `duality' concerns ChungYao interpolation at the intersections of any
% k of a given set of r hyperplanes in \Rk vs the Hakopian interpolation to mean
% values over the convex hulls of any k of a given set of r points in \Rk .

%Hakopian84a
% carl
\refJ Hakopian,  Hakop;
On multivariate spline functions, B-spline bases and
polynomial interpolation II;
\SM; 79; 1984; 91--102;

%Hakopian84b
% carl
\refJ Hakopian,  H.;
Multivariate interpolation II of Lagrange and Hermite type;
\SM; 80; 1984; 77--88;

%Hakopian85
% carl
\refP Hakopian,  H.;
Interpolation by polynomials and natural splines on normal lattices;
\MvatIII; 218--220;

%HakopianSaakyan94
% author
\refJ Akopyan,  A. A., Saakyan, A. A.;
Multivariate splines and polynomial interpolations;
Uspekhi Mat.\ Nauk; xxx; 1994; xxx--xxx;

%Handscomb91
% .
\refR Handscomb,  D. C.;
Interpolation and differentiation of multivariate functions and interpolation
of divergence free vector fields using surface splines;
Report 91/5, Oxford University Computing Laboratory, Numerical Analysis Group,
11 Keble Road (Oxford OX1 3QD); 1991;

%Haussmann79
\refP Haussmann,  W.;
On a multivariate Rolle type theorem and the interpolation remainder
formula;
\MvatI; 137--145;

%HaussmannPottinger77
% sonya
\refJ Haussmann,  W., Pottinger, P.;
On the construction and convergence of multivariate
interpolation operators;
\JAT; 19; 1977; 205--221;

%HolligMarsdenRiemenschneider89
\refJ H\"ollig,  K., Marsden, M. J., Riemenschneider, S. D.;
Bivariate cardinal interpolation on the 3-direction mesh: $\ell^p$-data;
\RMJM; 19; 1989; 189--198;

%Jetter83a
% larry
\refP Jetter,  K.;
Some contributions to bivariate interpolation and cubature;
\TexasIV; 533--538;

%Jetter92a
% larry
\refP Jetter,  K.;
Multivariate approximation from the 
cardinal interpolation point of view;
\TexasVII; 131--161;

%Jia86c
\refJ Jia,  Rong-Qing;
Extension of Kergin interpolation operators;
Ke Xue Tong Bao; 31; 1986; 805--808;

%JiaSharma91 
% sherm, author correction
\refJ Jia,  Rong-Qing, Sharma, A.;
Solvability of some multivariate interpolation problems;
J. reine angew.\ Math.; 421; 1991; 73--81;

%JinLiangXZ92a
% author
\refQ Jin, G. R., Liang, Xue-Zhang;
On convergence of Hakopian interpolation;
(Proceedings of a Symposium of the Mathematical Sciences,
dedicated to the 40th Anniversary of the Founding of the Department of
Mathematics), xxx (ed.), Jilin University (in Changchun, China); 1992; 278--280;

%KaznoNinomiys78
\refJ Kazno,  H., Ninomiys, J.;
An algorithm and error analysis of bivariate interpolating splines;
Dzexo.\ Cepn.; 19; 1978; 196--203;

%Kergin78
% carl
\refD Kergin,  P.;
Interpolation of $C^k$ Functions;
University of Toronto, Canada; 1978;

%Kergin80
% sonya
\refJ Kergin,  P.;
A natural interpolation of $C^k$ functions;
\JAT; 29; 1980; 278--293;

%Lai91b
\refR Lai,  M.-J.;
On fundamental solutions for multivariate singular interpolation;
Univ.\ of Utah; 1991;

%LaiWang84
% carl
\refJ Lai,  Mingjun, Wang, Xinghua;
 A note to the remainder of a multivariate interpolation polynomial;
\JATA; 1(1); 1984; 57--63;

%LascauxLesaint75
% .
\refJ Lascaux,  P., Lesaint, P.;
Some nonconforming finite elements for plate bending problems;
\RAIROAN; 9; 1975; 9--53;
% nonconforming, FEM, multivariate, polynomial interpolation, de Veubeke

%LiangXZ79a
% .
\refJ Liang,  Xhuezhang;
Properly posed nodes for bivariate interpolation and the superposed
interpolation (Chinese);
Jilin Daxue Xuebao, J.\ Jilin University (Natural Sciences); 1; 1979; 27--32;

%LiangXZ85
\refR Liang,  X. Z.;
On Hakopian interpolation in the disk;
Jilin; 1985;

%LiangXZ86
% author
\refJ Liang, Xue-Zhang;
On Hakopian interpolation in the disk;
\ATA; 1; 1986; 37--45;

%LiangXZ86
% .
\refJ Liang,  X. Z.;
Kergin-interpolation at the points which are zeros of the bivariate polynomial
of least deviation from zero on the disk (Chinese);
Dongbei Shida Xueboa, (Ziran Kexue Ban), J. Northeast Normal U. of Natural
Sciences, Changchun; 2; 1986; 408--414;
% Shayne

%LiangXZ89a
% author
\refJ Liang, Xue-Zhang;
Lagrange representation of multivariate interpolation;
Science in China (Ser.\ a); 4; 1989; 385--396;

%LiangXZLi91a
% author
\refJ Liang, Xue-Zhang, Li, L. Q.;
On bivariate osculatory interpolation;
\JCAM; 38; 1991; 271--282;

%LiangXZYe86
% author
\refJ Liang, Xue-Zhang, Ye, Y. M.;
On Kergin interpolation at the points which are zeros of the bivariate
polynomial of least deviation from zero on the disk;
Northeastern Math.\ J.; 4; 1986; 409--414;

%Lorenc81
\refJ Lorenc,  A. C.;
A global three dimensional multivariate
statistical interpolation scheme;
Mon.\ Wea.\ Rev.; 109; 1981; 701--721;

%LorentzG87b
\refP Lorentz,  G. G.;
On the determinant of a bivariate Birkhoff interpolation problem;
\ShrivenhamI; 169--179;

%LorentzG89
% carl
\refJ Lorentz,  G. G.;
Solvability of multivariate interpolation;
J. reine angew.\ Math.; 398; 1989; 101--104;

%LorentzG89b
\refJ Lorentz,  G. G.;
Uniform bivariate Hermite interpolation I: Coordinate degree;
\MZ; 203; 1990; 193--210;

%LorentzGLorentzR85
% carl
\refQ Lorentz,  G. G., Lorentz, R. A.;
Multivariate interpolation;
(Rational Approximation and interpolation),
P. R. Graves-Morris {\sl et al} (eds.),
Lecture Notes in Math.\ 1105, Springer-Verlag (Berlin); 1985; 136--144;

%LorentzGLorentzR86
\refR Lorentz,  G. G., Lorentz, R. A.;
Three papers on bivariate Birkhoff interpolation;
GMD; 1986;

%LorentzGLorentzR86b
% greg
\refJ Lorentz,  G. G., Lorentz, R. A.;
Solvability problems of bivariate interpolation I;
\CA; 2; 1986; 153--169;

%LorentzGLorentzR87
\refJ Lorentz,  G. G., Lorentz, R. A.;
Solvability of bivariate interpolation, II:  Applications;
\JATA; 3; 1987; 79--97;

%LorentzGLorentzR90
% carl
\refJ Lorentz,  G. G., Lorentz, R. A.;
Bivariate Hermite interpolation and applications to algebraic geometry;
\NM; 57; 1990; 669--690;

%LorentzR84
\refP Lorentz,  R. A.;
Some regular problems of bivariate interpolation;
\VarnaI; 549--562;

%LorentzR88
\refR Lorentz,  R. A.;
Uniform bivariate Hermite interpolation I: Coordinate degree;
GMD; 1988;

%LorentzR88b
\refR Lorentz,  R. A.;
Uniform bivariate Hermite interpolation II: Total degree;
GMD; 1988;

%LorentzR92
% carl
\refB Lorentz,  R. A.;
Multivariate Birkhoff Interpolation;
Lecture Notes in Mathematics, No.\ 1516, Springer Verlag (Heidelberg); 1992;

%MadychNelson83
\refR Madych,  W. R., Nelson, S. A.;
Multivariate interpolation: a variational theory; 
unpublished mansucript; 1983;

%MadychNelson88
% larry
\refJ Madych,  W. R., Nelson, S. A.;
Multivariate interpolation and conditionally positive definite functions; 
\ATA;  4; 1988; 77--89;

%MadychNelson90b
% carl
\refJ Madych, W. R., Nelson, S. A.;
Multivariate interpolation and conditionally positive definite functions.II; 
\MC; 54(189); 1990; 211--230;

%MadychNelson92
% carl
\refJ Madych,  W. R., Nelson, S. A.;
Bounds on multivariate polynomials and exponential error estimates for
multiquadric interpolation;
\JAT; 70; 1992; 94--114;

%Maier94
% .
\refD Maier, Ulrike;
Approximation durch Kergin-Interpolation;
Dr., Universit\"at Dortmund (Germany); 1994;
% represent interpolant in power form

%Mason82
\refR Mason,  J. C.;
Minimal projections and near-best approximations by multivariate polynomial
expansion and interpolation;
RCMS; 1982;

%Meinguet79b
% carl
\refJ Meinguet,  J.;
Multivariate interpolation at arbitrary points made simple;
\ZAMP; 30,1; 1979; 292--304;
% thin-plate, $D^m$-splines

%Meinguet79c
% carl
\refP Meinguet,  J.;
An intrinsic approach to multivariate spline interpolation at arbitrary points;
\Sahney; 163--190;
% thin-plate, $D^m$-splines

%Melkes72
% carl
\refJ Melkes, Franti\v sek;
Reduced piecewise bivariate Hermite interpolations;
\NM; 19; 1972; 326--340;

%MeyerWW70a
% larry
\refR Meyer,  W. W.;
A note on remainders of the derivative mean-value type in multivariate
polynomial interpolation;
GM; 1970;

%Micchelli80b
% larry
\refJ Micchelli,  C. A.;
A constructive approach to Kergin interpolation in $\RR^k$:
multivariate B-splines and Lagrange interpolation;
\RMJM; 10; 1980; 485--497;

%MicchelliMilman80
% sonya
\refJ Micchelli,  C. A., Milman, P.;
A formula for Kergin interpolation in $\RR^k$;
\JAT; 29; 1980; 294--296;

%Morsche86
\refR Morsche,  H. G. ter;
Bivariate cubic periodic spline interpolation on a three
direction mesh;
Rpt.\ 86-WSK-02, Univ.\ Eindhoven; 1986;

%Morsche87
\refP Morsche,  H. G. ter;
Attenuation factors and multivariate periodic spline interpolation;
\Chile; 165--174;

%MuhlbachGasca91
% sherm, update page numbers
\refJ M\"uhlbach,  G., Gasca, M.;
Multivariate polynomial interpolation under projectivities Part I:
Lagrange and Newton interpolation formulas;
\NA; 1; 1991; 375--399;

%Mulansky99b
\refR Mulansky,  B.;
Interpolation of scattered data by a bivariate convex function I: 
Piecewise linear $C^0$-interpolation;
Report 858, Twente; xxx;

%Nadler90
% carl
\refQ Nadler, Edmond;
Hermite interpolation by $C^1$ bivariate splines;
(Contributions to the Computation of Curves and Surfaces), W. Dahmen,
M. Gasca, and Charles A. Micchelli (eds.), Monografias de la Academia de
Ciencias de Zaragoza (Spain); 1990; 55--66;
% see Nadler87

%Nadler90
% carl
\refQ Nadler, Edmond;
Hermite interpolation by $C^1$ bivariate splines;
(Contributions to the Computation of Curves and Surfaces), W. Dahmen,
M. Gasca, and Charles A. Micchelli (eds.), Monografias de la Academia de
Ciencias de Zaragoza (Spain); 1990; 55--66;
% see Nadler87

%Nielson74c
% carl
\refJ Nielson,  Gregory M.;
Multivariate smoothing and interpolating splines;
\SJNA; 11; 1974; 435--446;

%Nielson83
% carl
\refJ Nielson, Gregory M.;
A method for interpolation of scattered data based upon
a minimum norm network;
\MC; 40(161); 1983; 253--271;
% bivariate interpolation, random data interpolation, splines, 
% multivariate approximation and interpolation.

%NurnbergerRiessinger92
\refJ N\"urnberger,  G., Riessinger, Th.;
Lagrange and Hermite interpolation by bivariate splines;
\NFAO; 13; 1992; 75--96;

%Paskov92
% carl
\refJ Paskov,  Spassimir H.;
Singularity of bivariate interpolation;
\JAT; 70; 1992; 50--67;
% concerns total degree interpolation to total-degree Hermite data at one or
% more points.\ Choice N:= (n_1,...,n_s, n) of the degrees of the Hermite data 
% and of the polynomial interpolant is {\bf regular} if there is at least one 
% choice of points for which this is a correct interpolation problem.\ If 
% \sum_j dim\Pi_j < \dim \Pi_n , problem is obviously singular.\ Guess is that
% any singular N is necessarily the (vector) sum of such obviously singular 
% ones.\ See also  GevorgianHakopianSaakyan92a

%Radon48
% .
\refJ Radon,  J.;
Zur mechanischen Kubatur;
Monatshefte der Math.; 52(4); 1948; 286--300;
% first paper on multivariate polynomial interpolation giving a large
% class of points correct for interpolation by total degree polynomials.

%Renka81
% larry
\refD Renka,  R. J.;
Triangulation and bivariate interpolation for
irregularly distributed data points;
Univ.\ Texas; 1981;

%Rescorla85
% larry
\refD Rescorla,  K. L.;
Multivariate interpolation;
Univ.\ Utah; 1985;

%Riemenschneider89
% larry
\refP Riemenschneider,  Sherman D.;
Multivariate cardinal interpolation;
\TexasVI;
561--580;

%Roulier85
\refR Roulier,  J. A.;
A convexity preserving grid refinement algorithm for interpolation
of bivariate functions;
Rpt.\ Univ.\ Connecticut; 1985;

%Salzer57
% larry
\refJ Salzer, H. E.;
Note on multivariate interpolation for uneqally spaced arguments, with
an application to double summation;
\SJAM; 5; 1957; 254--262;

%Salzer71
% larry, carl
\refJ Salzer, Herbert E.;
Formulas for bivariate hyperosculatory interpolation;
\MC; 25(113); 1971; 119--133;
% Cartesian interpolation, remainder formulas.

%SauerXu93
% .
\refR Sauer,  T., Xu, Yuan;
On multivariate Lagrange interpolation; ms; 1993;

%Schultz69b
% sonya
\refJ Schultz,  M. H.;
Multivariate $L-$spline interpolation;
\JAT; 2; 1969; 127--135;

%Schultz73c
% sonya
\refJ Schultz,  M. H.;
Error bounds for a bivariate interpolation scheme;
\JAT; 8; 1973; 189--194;

%Shi84
% .
\refJ Shi,  Z. C.;
The generalized patch test for Zienkiewicz's triangles;
J. Comput.\ Math.; 1; 1984; 279--286;
% nonconforming, FEM, multivariate, polynomial interpolation

%Shi86
% .
\refJ Shi,  Z. C.;
A unified formation of shape functions for two kinds of nonconforming plate
bending elements;
Numer.\ Math.\ Sinica; 8; 1986; 428--434;
% nonconforming, FEM, multivariate, polynomial interpolation

%Shi87
% ., carl
\refJ Shi, Zhong-Ci;
The F-E-M-Test for convergence of nonconforming finite elements;
\MC; 49(180); 1987; 391--405;
% nonconforming, FEM, multivariate, polynomial interpolation.

%ShiChen90
% .
\refJ Shi,  Z. C., Shen, S. C.;
A direct analysis of the 9-parameter quasi-conforming plate element;
Numer.\ Math.\ Sinica; 12; 1990; 76--84;
% nonconforming, FEM, multivariate, polynomial interpolation

%Sibson81
\refQ Sibson,  R.;
A brief description of natural neighbor interpolation;
(Interpreting Multivariate Data),
D. V. Barnett (ed.), Wiley (New York); 1981; 21--36;

%Sivakumar90a
% sonya
\refJ Sivakumar,  N.;
On bivariate cardinal interpolation by shifted splines on a 
three-direction mesh;
\JAT; 61; 1990; 178--193;

%Specht88
% .
\refJ Specht,  B.;
Modified shpae functions for the three-node plate bending element passing the
patch test;
\IJNME; 26; 1988; 705--715;
% nonconforming, FEM, multivariate, polynomial interpolation

%Stockler89a
\refP St\"ockler,  J.;
Cardinal interpolation with translates of shifted bivariate box-splines;
\Oslo; 583--592;

%Stockler91
% greg
\refJ St\"ockler,  J.;
Multivariate Bernoulli splines and the periodic interpolation problem;
\CA;  7; 1991; 105--122;

%SunX90
% author
\refD Sun,  Xingping;
Multivariate interpolation using ridge or related functions;
The University of Texas at Austin, August; 1990;

%SunX93
% carl
\refJ Sun,  Xingping;
Solvability of multivariate interpolation by radial or related functions;
\JAT; 72(3); 1993; 252--267;

%TaylorSimoZienkiewiczChan86
% .
\refJ Taylor,  R. L., Simo, J. C., Zienkiewicz, O. C., Chan, A. C. H.;
The patch test -- a condition for assessing FEM convergence;
\IJNME; 22; 1986; 39--52;
% nonconforming, FEM, multivariate, polynomial interpolation

%WangLai86
% carl
\refJ Wang, Xinghua, Lai,  Mingjun;
 On multivariate Newtonian interpolation;
 Sci.\ Sinica.\ Ser.\ A; 29(1); 1986; 23--32;

%WangR75a
\refJ Wang,  Ren-hong;
Structure of multivariate splines and interpolation (Chinese);
Acta Math.\ Sinica; 18; 1975; 95--106;
% another version of the title is: The structural characterization and 
% interpolation for multivariate splines, pages 91--106.

%WangR75b
\refJ Wang,  R. H.;
The structural characterization and interpolation for
multivariate splines (Chinese);
Acta Math.\ Sinica; 18; 1975; 91--106;

%Watson85
\refQ Watson, G. S.;
Interpolation and smoothing of directed and undirected line data;
(Multivariate Analysis - VI), P. R. Krishnaiah (ed.), Elsevier (Amsterdam);
1985; 613--625;

%Werner80
\refJ Werner,  H.;
Remarks on Newton--type multivariate interpolation for subsets of grids;
\C; 25; 1980; 181--191;

%Wu88
\refJ Wu,  Zong Min;
A suitable method for the interpolation of multivariate scattered data, 
and its convergence rate;
Chinese Quarterly Journal of Mathematics;
3;
1988;
105--110;

%Xiong89
% carl
\refP Xiong,  Zhen-xiang;
Multivariate interpolating polynomials;
\TexasVI; 679--682;

%Xiong92
% carl
\refJ Xiong,  Zhenxiang;
Bivariate interpolating polynomials and splines (I);
\JATA; 8(2); 1992; 49--66;

%XiongCuiLi89
\refR Xiong,  Z.-X., Cui, D.-Y., Li, X.-Y.;
Multivariate interpolating polynomials and splines;
Beijing Univ.\ of Aeronautics \& Astronautics; xxx;

%Xu92a
% carl
\refJ Xu, Yuan;
Gaussian cubature and bivariate polynomial interpolation;
\MC; 99(200); 1992; 547--555;
% common zeros of quasi-orthogonal polynomials.

%Zhang89a
\refJ Zhang,  Zuo Shun;
 A multivariate cardinal interpolation problem;
Chinese Annals of Mathematics.\ Series A;
10;
1989;
581--587;

%ZhangHQ83
% .
\refQ Zhang,  H. Q.;
The generalized patch and 9-parameter quasi-conforming element;
(Proc.\ China-France symposium on finite element methods), Feng Kang and J. L.
Lions (eds.), Science Press, Gordon and Breach (xxx); 1983; 566--583;
% nonconforming, FEM, multivariate, polynomial interpolation

%ZhouChangHe84
% author
\refJ Zhou,  Y. S., Chang, Y. T., He, Tian-Xiao;
On multivariate interpolations;
Engineering Mathematics; 1; 1984; 12--16;