\documentclass[seceqn,secthm,ACO]{baltzer}
\usepackage{amsfonts}
\def\RR{{\mathbb R}}
%Multivariate polynomial interpolation references
\begin{document}
\begin{thebibliography}{000} %{00} for numbered bibliography



\bibitem{BerezinZhidkov65}
I.~S. Berezin and N.~P. Zhidkov.
\newblock {\em Computing Methods}.
\newblock Addison--Wesley, 1965.
\newblock Russian version in 1959.



\bibitem{Birkhoff79}
G.~Birkhoff.
\newblock The algebra of multivariate interpolation.
\newblock In C.V. Coffman and G.J. Fix, editors, {\em Constructive
Approaches to Mathematical Models}, pages 345--363. Academic Press
Inc., 1979.

\bibitem{BojanHakop93}
B.~Bojanov, H.~A. Hakopian and A.~Sahakian.
\newblock {\em Spline functions and multivariate interpolation},
\newblock Kluwer Academic  Publishers, 1993.

\bibitem{deBoor82}
C.~de Boor.
\newblock Topics in multivariate approximation theory.
\newblock In {\em Topics in Numerical Analysis}, Lect. Not. Math. {\bf
965}, pages 39--78. Birkh\"auser Verlag, 1982.

\bibitem{deBoor94}
C.~de Boor.
\newblock Gauss elimination by segments and multivariate polynomial
  interpolation.
\newblock In R.~V.~M. Zahar, editor, {\em Approximation and
Computation: A Festschrift in Honor of Walter Gautschi}, pages
87--96. Birkh\"auser Verlag, 1994.

\bibitem{deBoor94a}
C.~de Boor.
\newblock Polynomial interpolation in several variables.
\newblock In R.~de Millo and J.~R. Rice editors, {\em Studies in Computer Science}
, pages 87--119. Plenum Press, 1994.


\bibitem{deBoor95}
C.~de Boor.
\newblock A multivariate divided difference.
\newblock In C.~K. Chui and L.~L. Schumaker, editors, {\em Approximation Theory
  VIII, Vol.~1: Approximation and Interpolation}, pages 87--96. World
  Scientific Publishing Co., 1995.

\bibitem{deBoor96}
C.~de Boor.
\newblock On the {S}auer--{X}u formula in multivariate polynomial
  interpolation.
\newblock {\em Math. Comp.}, {\bf 65}~(1996),~1231--1234.

\bibitem{deBoor97}
C.~de Boor.
\newblock The error in polynomial tensor-product, and in {C}hung-{Y}ao,
  interpolation.
\newblock In A.~Le~M\'{e}haut\'{e}, C.~Rabut, and L.~L. Schumaker, editors, {\em
  Surface Fitting and Multiresolution Methods}, pages 35--50. Vanderbilt
  University Press, 1997.

\bibitem{deBoor99}
C.~de Boor.
\newblock Computational aspects of multivariate polynomial interpolation:
Indexing the coefficients.
\newblock This volume.

\bibitem{deBoorRon90}
C.~de Boor and A.~Ron.
\newblock On multivariate polynomial interpolation.
\newblock {\em Constr. Approx.}, {\bf 6}~(1990),~287--302.

\bibitem{deBoorRon92}
C.~de Boor and A.~Ron.
\newblock Computational aspects of polynomial interpolation in several
  variables.
\newblock {\em Math. Comp.}, {\bf 58}~(1992),~705--727.

\bibitem{deBoorRon92a}
C.~de Boor and A.~Ron.
\newblock The least solution for the polynomial interpolation problem.
\newblock {\em Math. Z.}, {\bf 210}~(1992),~347--378.

\bibitem{Bos90}
L.~Bos.
\newblock On certain configurations of points in $\RR^n$ which are
unisolvent for polynomial interpolation.
\newblock {\em SIAM J. Approx. Theo.}, {\bf 64}~(1991),~271--280.


\bibitem{Buchberger85}
B.~Buchberger.
\newblock Gr\"obner bases: an algorithmic method in polynomial ideal theory.
In N.~K.~Bose, editor, {\em Multidimensional System Theory}, pages
184--232, Reidel, 1985.



\bibitem{BuchbergerMoeller82}
B.~Buchberger and  H.~M.~M\"oller.
\newblock The construction of multivariate polynomials with preassigned zeros.
\newblock In G.~Goos and J.~Hartmanis, editors, {\em Computer Algebra,
{EUROCAM} '82, European Computer Algebra Conference}, pages
24--31, Springer Lecture Notes in Computer Science {\bf 144},
1982.

\bibitem{Busch85}
J.~R. Busch.
\newblock Osculatory interpolation in $\RR^n$.
\newblock {\em SIAM J. Num. Anal.}, {\bf 22}~(1985),~107--113.

\bibitem{Busch90}
J.~R. Busch.
\newblock A note on Lagrange interpolation in $\RR^2$..
\newblock {\em Rev. Union Matem. Argent.}, {\bf 36}~(1990),~33--38.

\bibitem{CDM80}
A.~L.~Cavaretta, C.~A.~Micchelli and A.~Sharma.
\newblock Multivariate interpolation and the Radon transform.
\newblock {\em Math. Z.}, {\bf 174}~(1980),~263--279.


\bibitem{CarniGasca89a}
J.~M. Carnicer and M.~Gasca.
\newblock On finite element interpolation problems.
\newblock  In T.~Lyche and L.~L. Schumaker, editors, {\em
  Mathematical Methods in Computer Aided Geometric Design},
   pages 105--113. Academic Press, 1989.

\bibitem{CarniGasca89b}
J.~M. Carnicer and M.~Gasca.
\newblock On the evaluation of multivariate Lagrange formulae.
\newblock In W. Schemp
edit.,{\em Multivariate Approximation Theory IV},  pages 65--72.
Birkhauser V., 1989.

\bibitem{CarniGasca90}
J.~M. Carnicer and M.~Gasca.
\newblock Evaluation of multivariate polynomials and their derivatives.
\newblock {\em Math.  Comp.}, {\bf 54}~(1990),~231--244.

\bibitem{ChuiLai88}
C.~K. Chui and M.~J. Lai.
\newblock Vandermonde determinants and Lagrange interpolation in
$\RR^s$.
\newblock  In  B.~L Lin, editor, {\em
  Nonlinear and Convex Analysis}. Marcel Dekker, 1988.

\bibitem{Chui88}
C.~K. Chui.
\newblock Multivariate Splines.
\newblock  CBMS--NSF Regional Conference Series in Applied Mathematics
{\bf 54}, SIAM, 1988.

\bibitem{ChungYao77}
K.~C. Chung and T.~H. Yao.
\newblock On lattices admitting unique {L}agrange interpolation.
\newblock {\em SIAM J. Num. Anal.}, {\bf 14}~(1977),~735--743.

\bibitem{CiarletRaviart72}
P.~G. Ciarlet and P.~A. Raviart.
\newblock General {L}agrange and {H}ermite interpolation in {$\RR^n$} with
  applications to finite element methods.
\newblock {\em Arch. Rational Mech. Anal.}, {\bf 46}~(1972),~178--199.

\bibitem{Ciarlet78}
P.~G. Ciarlet.
\newblock {\em The finite element method for elliptic problems}.
\newblock North Holland, 1978.


\bibitem{CiarletWagschal71}
P.~G. Ciarlet and C.~Wagschal.
\newblock Multipoint Taylor formulas and
  applications to the finite element method.
\newblock {\em Num. Math.}, {\bf 17}~(1971),~84--100.

\bibitem{Coatmelec66}
C.~Coatmelec.
\newblock Approximation et  interpolation des fonctions differentiables
de plusieurs variables.
\newblock {\em Ann. Sci. Ecole Norm. Sup.}, {\bf 83}~(1966),~271--341.




\bibitem{Davis75}
P.~J. Davis.
\newblock {\em Interpolation and approximation}.
\newblock Dover Pub., 1975.

\bibitem{DynRon90}
N.~Dyn and A.~Ron.
\newblock On multivariate polynomial interpolation.
\newblock In J.~C. Mason  and M.~E. Cox  editors,
{\em Algorithms for Approximation II}, pages 177--184. Chapman and
Hall, 1990.


\bibitem{Gasca90}
M.~Gasca.
\newblock Multivariate polynomial interpolation.
\newblock In W.~Dahmen, M.~Gasca, and C.~A. Micchelli, editors, {\em
  Computation of Curves and Surfaces}, pages 215--236. Kluver Academic
  Publishers, 1990.

\bibitem{GascaLebron}
M.~Gasca and E.~Lebr\'{o}n.
\newblock On Aitken- Neville formulae for multivariate interpolation.
\newblock In E.~L. Ortiz editor,
 {\em Numerical approximation of partial differential equations },
  pages 133--140. North Holland, 1987.


\bibitem{GascaLopez82}
M.~Gasca and A.~L{\'{o}}pez-Carmona.
\newblock A general recurrence interpolation formula and its applications to
  multivariate interpolation.
\newblock {\em J. Approx. Theory}, {\bf 34}~(1982),~361--374.

\bibitem{GascaMaeztu82}
M.~Gasca and J.~I. Maeztu.
\newblock On {L}agrange and {H}ermite interpolation in {$\RR^k$}.
\newblock {\em Numer. Math.}, {\bf 39}~(1982),~1--14.

\bibitem{GascaMartinez87}
M.~Gasca and J.~J. Mart\'inez.
\newblock On the computation of multivariate confluent Vandermonde
 determinants and its applications .
\newblock In R.~Martin, editor, {\em The Mathematics of surfaces II},
 pages 101--114, Oxford Univ. Press, 1987.

\bibitem{GascaMartinez90}
M.~Gasca and J.~J. Mart\'inez.
\newblock On the solvability of bivariate {H}ermite--{B}irkhoff interpolation
  problems.
\newblock {\em J, Comput. and Appl. Math.}, {\bf 32}~(1990),~77--82.

\bibitem{GascaMuhl88}
M.~Gasca and G.~M\"{u}hlbach.
\newblock Multivariate interpolation: a survey with regard to extrapolation.
\newblock In {\em Proceedings IMACS Transactions on scientific computing},
{\bf vol. 1}, pages 255--278,Paris,~(1988).

\bibitem{GascaMuhl92}
M.~Gasca and G.~M\"{u}hlbach.
\newblock Multivariate polynomial interpolation under
projectivities II: Aitken-Neville formulas.
\newblock {\em Numer. Algor.}, {\bf 2}~(1992)~ 255--278.

\bibitem{GascaRamirez84}
M.~Gasca and V.~Ramirez.
\newblock Interpolation systems in {$\RR^k$}.
\newblock {\em J. Approx. Theory}, {\bf 42}~(1984)~36--51.

\bibitem{GascaSauer97P}
M.~Gasca and T.~Sauer.
\newblock On bivariate {H}ermite interpolation with minimal degree
polynomials.
\newblock ~(1998).
\newblock submitted for publication.

\bibitem{Gevorgian95}
H.~V. Gevorgian, H.~A. Hakopian and A.~A. Sahakian.
\newblock On the bivariate Hermite interpolation problem.
\newblock {\em Constr. Approx.}, {\bf 11}~(1995)~23--35.

\bibitem{Glaeser71}
G.~Glaeser.
\newblock L'interpolation des fonctions differentiables
de plusieurs variables.
\newblock In  {\em Proc. Liverpool Singularities Symposium  II},
 pages 1--29, Lect. Not. Math. {\bf 209}. Springer V. 1971.

\bibitem{Gout77}
J.~L.~Gout.
\newblock Estimation de l'erreur d'interpolation d'Hermit dans $\RR^n$.
\newblock {\em Numer. Math.}, {\bf 28}~(1977)~407--429.

\bibitem{Groebner}
W.~Gr\"obner.
\newblock Algebraische Geometrie {I}, {II}.
\newblock Bibliographisches Institut Mannheim, B.I--Hochschultaschenb{\"{u}}cher,
1968 and 1970.

\bibitem{GuentRoet}
R.~B. Guenter and E.~L. Roetman.
\newblock Some observations on interpolation in higher dimensions.
\newblock {\em Math.Comp.}, {\bf 24}~(1970)~517--521.

\bibitem{Habib96}
A.~W. Habib, R.~N. Goldman and T.~Lyche.
\newblock A recursive algorithm for  Hermite interpolation over a
triangular grid.
\newblock {\em J. Comp. Appl. Math.}, {\bf 73}~(1996)~95--118.

\bibitem{Hack}
F.~Hack.
\newblock On bivariate Birkhoff interpolation.
\newblock {\em J. Approx. Th.}, {\bf 49}~(1987)~18--30.

\bibitem{Hakopian82}
H.~A. Hakopian.
\newblock Multivariate divided differences and
multivariate interpolation of Lagrange and Hermite type.
\newblock {\em J. Approx. Th.}, {\bf 34}~(1982)~286--305.

\bibitem{IsaacsonKeller66}
E.~Isaacson and H.~B. Keller.
\newblock {\em Analysis of Numerical Methods}.
\newblock John Wiley \& Sons, 1966.

\bibitem{Jetter83}
K.~Jetter.
\newblock Some contributions to bivariate interpolation and
cubature.
\newblock In C.~K. Chui, L.~L. Schumaker and J.~D. Ward, editors,
{\em Approximation Theory IV}, pages 533--538, Academic Press,
1983.

\bibitem{Kergin}
P.~Kergin.
\newblock A natural  interpolation of $C^k$ functions.
\newblock {\em J. Approx. Th.}, {\bf 29}~(1980)~278--293.

\bibitem{KinCheney91}
D. Kincaid and W. Cheney.
\newblock {\em  Numerical Analysis}.
\newblock Brooks/Cole Pub., 1991.

\bibitem{Kronecker1865}
L.~Kronecker.
\newblock {\"{U}}ber einige {I}nterpolationsformeln f{\"{u}}r ganze {F}unktionen
  mehrerer {V}ariabeln.
\newblock In H.~Hensel, editor, {\em L.~Kroneckers Werke}, volume~I, pages
  133--141. Chelsea Publishing Company, 1865.
\newblock Lecture at the academy of sciences, December 21, 1865.

\bibitem{Kunz57}
K.S. Kunz.
\newblock {\em Numerical Analysis}.
\newblock McGraw-Hill Book Company, 1957.

\bibitem{LeePhil88}
S.~L. Lee and G.~M. Phillips.
\newblock Polynomial interpolation at points of a geometric mesh
on a triangle.
\newblock {\em Proc. Roy. Soc. Edinburgh}, {\bf 108A }~(1988),~75--87.


\bibitem{LeePhilCA}
S.~L. Lee and G.~M. Phillips.
\newblock Construction of lattices for Lagrange interpolation
in Projective space.
\newblock {\em Constructive Approximation}, {\bf }~(1990??),~--.

\bibitem{LeMehau90}
A.~Le~M\'{e}haut\'{e}.
\newblock A finite element approach to surface reconstruction.
\newblock In W.~Dahmen, M.~Gasca, and C.~A. Micchelli, editors, {\em
  Computation of Curves and Surfaces}, pages 237--274. Kluver Academic
  Publishers, 1990.

\bibitem{LeMehau99}
A.~Le~M\'{e}haut\'{e}.
\newblock On some aspects of multivariate polynomial interpolation.
\newblock This volume.

\bibitem{Lodha97}
S.~K. Lodha and R.~N. Goldman.
\newblock A unified approach to  evaluation algorithms  for
multivariate polynomials.
\newblock {\em Math. Comp.} {\bf 66}~(1997)~1521--1553.

\bibitem{LorenteRamirez}
J.~Lorente and V.~Ram\'{\i}rez.
\newblock On interpolation systems and H-reducible interpolation problems.
\newblock In C.~K. Chui, L.~L. Schumaker, and F.~Utreras, editors, {\em
  Topics in multivariate approximation}, pages 153--163.  Academic
  Press, 1987.

\bibitem{Lorentz66}
G.~G. Lorentz.
\newblock {\em Approximation of functions}.
\newblock Chelsea Publishing Company, 1966.

\bibitem{LoJeRi}
G.~G. Lorentz, K. Jetter and S.~D. Riemenschneider.
\newblock {\em Birkhoff interpolation}.
\newblock Addison-Wesley,1983.

\bibitem{Lorentz92}
R.~A. Lorentz.
\newblock {\em Multivariate Birkhoff Interpolation}.
\newblock Number 1516 in Lecture Notes in Mathematics. Springer Verlag, 1992.


\bibitem{Maeztu82}
J.~I. Maeztu.
\newblock Divided differences associated with reversible systems
in $\RR^2$.
\newblock {\em Computing}, {\bf 40}~(1988)~1032--1040.

\bibitem{Mairhuber}
J.~C. Mairhuber.
\newblock On Haar's Theorem concerning Chebychev approximation problems having
unique solutions.
\newblock {\em Proceedings of the A.M.S.}, {\bf 7}~(1956)~609--615.


\bibitem{Micchelli79}
C.~A. Micchelli.
\newblock On a numerically efficient method of computing multivariate
  {B}--splines.
\newblock In W.~Schempp and K.~Zeller, editors, {\em Multivariate Approximation
  Theory}, pages 211--248. Birkh\"auser, Basel, 1979.

\bibitem{Micchelli80}
C.~A. Micchelli.
\newblock A constructive approach to {K}ergin interpolation in {$\RR^k$}:
  multivariate {B}--splines and {L}agrange interpolation.
\newblock {\em Rocky Mountain J. Math.}, {\bf 10}~(1979),~485--497.

\bibitem{MicchelliMilman}
C.~A. Micchelli and P.~Milman.
\newblock A formula for Kergin  interpolation in $\RR^k$.
\newblock {\em J. Approx. Th.}, {\bf 29}~(1980)~294--296.

\bibitem{Micchelli86}
C.~A. Micchelli.
\newblock Algebraic aspects of  interpolation.
\newblock In C. de Boor, editor,{\em Approximation Theory}, Proc. Symp.
Appl. Math,  {\bf 36}, pages 81--102, Amer. Math. Soc., 1986.



\bibitem{MicchelliSauerXu98}
C.~A. Micchelli, T.~Sauer, and Yuesheng Xu.
\newblock A construction of refinable sets for interpolating wavelets.
\newblock {\em Results in Mathematics}, {\bf 34}~(1998),~359--372.

\bibitem{Moller77}
H.~M. M\"{o}ller.
\newblock  Hermite interpolation in several variables
using ideal-theoretic methods.
\newblock In W.~ Schempp and K.~ Zeller editors,
{\em Constructive Theory of Functions of Several Variables}, Lect.
Not. Math.{\bf 571}, pages 155--163, 1977.

\bibitem{Moeller98}
H.~M.~M\"oller.
\newblock {G}r{\"o}bner bases and Numerical Analysis.
\newblock In B.~Buchberger and F.~Winkler, editors, {\em Groebner Bases and
  Applications (Proc. of the Conf. 33 Years of Groebner Bases)}, volume 251 of
  {\em London Math. Soc. Lecture Notes}, pages 159--179. Cambridge University
  Press, 1998.

\bibitem{MoellerSauer99}
H.~M.~M\"oller and T.~Sauer.
\newblock H--bases for polynomial interpolation and system solving.
\newblock This volume.

\bibitem{Muhl88}
G.~M\"{u}hlbach.
\newblock On multivariate interpolation by generalized polynomials on subsets of
grids.
\newblock {\em Computing}, {\bf 40}~(1988).

\bibitem{MuhlGasca91}
G.~M\"{u}hlbach and M.~Gasca.
\newblock Multivariate interpolation under Projectivities I.
Lagrange and Newton interpolation formulas.
\newblock {\em Numer. Algor.}, {\bf 1}~(1991),~375--400.

\bibitem{Nicolaides72}
R.~A. Nicolaides.
\newblock On a class of finite elements generated by {L}agrange interpolation.
\newblock {\em SIAM J. Numer. Anal.}, {\bf 9}~(1972),~435--445.

\bibitem{Nicolaides73}
R.~A. Nicolaides.
\newblock On a class of finite elements generated by {L}agrange interpolation.
  {II}.
\newblock {\em SIAM J. Numer. Anal.}, {\bf 10}~(1973),~182--189.

\bibitem{PenaSauer99}
J.~M.~Pe{\~n}a and T.~Sauer.
\newblock On the multivariate Horner scheme.
\newblock {\em SIAM J. Numer. Anal.}, (1999), to appear.

\bibitem{Robbiano86}
L.~Robbiano.
\newblock On the theory of graded structures.
\newblock {\em J. Symbolic Computation}, {\bf 2}~(1986),~139--170.

\bibitem{Salzer64}
H.~E. Salzer.
\newblock Divided differences for functions of two variables for
irregularly spaced arguments.
\newblock {\em Numer. Math.}, {\bf 6}~(1964),~68--77.

\bibitem{Sauer95}
T.~Sauer.
\newblock Computational aspects of multivariate polynomial interpolation.
\newblock {\em Advances Comput. Math.}, {\bf 3}~(1995),~219--238.

\bibitem{Sauer97a}
T.~Sauer.
\newblock Polynomial interpolation of minimal degree.
\newblock {\em Numer. Math.}, {\bf 78}~(1997),~59--85.

\bibitem{Sauer98}
T.~Sauer.
\newblock Polynomial interpolation of minimal degree and {G}r{\"o}bner bases.
\newblock In B.~Buchberger and F.~Winkler, editors, {\em Groebner Bases and
  Applications (Proc. of the Conf. 33 Years of Groebner Bases)}, volume 251 of
  {\em London Math. Soc. Lecture Notes}, pages 483--494. Cambridge University
  Press, 1998.

\bibitem{Sauer99P}
T.~Sauer.
\newblock Gr\"obner bases, H--bases and interpolation.
\newblock {\em Trans. Amer. Math. Soc.}, to appear.

\bibitem{SauerXu95}
T.~Sauer and Yuan Xu.
\newblock On multivariate {L}agrange interpolation.
\newblock {\em Math. Comp.}, {\bf 64}~(1995),~1147--1170.

\bibitem{SauerXu95a}
T.~Sauer and Yuan Xu.
\newblock On multivariate {H}ermite interpolation.
\newblock {\em Advances Comput. Math.}, {\bf 4}~(1995),~207--259.

\bibitem{SauerXu96}
T.~Sauer and Yuan Xu.
\newblock Regular points for {L}agrange interpolation on the unit disk.
\newblock {\em Numer. Algo.}, {\bf 12}~(1996),~287-296.

\bibitem{Schumaker76}
L.~L. Schumaker.
\newblock Fitting surfaces to scattered data.
\newblock In G.~G. Lorentz. C.~K Chui and L.~L. Schumaker, editors,
{\em Approximation Theory 2}. Academic Press, 1976.


\bibitem{Steffensen}
I.~F. Steffensen.
\newblock {\em Interpolation}.
\newblock Chelsea, New York, 1927.

\bibitem{ThachMilne60}
H.~C. Thacher Jr. and W.~E. Milne.
\newblock Interpolation in several variables.
\newblock {\em J. SIAM}, {\bf 8}~(1960),~33--42.

\bibitem{Thacher60}
H.~C. Thacher Jr.
\newblock Derivation of interpolation formulas in several
independent variables.
\newblock {\em Annals New York Acad. Sc.}, {\bf 86}~(1960),~758--775.

\bibitem{Walker}
R.~S. Walker.
\newblock {\em Algebraic curves}.
\newblock Springer Verlag 1978.

\bibitem{Werner}
H.~Werner.
\newblock Remarks on Newton type multivariate interpolation
for subsets of grids.
\newblock {\em Computing}, {\bf 25}~(1980),~181--191.

\end{thebibliography}
\end{document}

--=====================_925837390==_--

