Some recent work and people involved David Handscomb (dch@comlab.oxford.ac.uk): using the variational calculus to get sharp L_2-bounds on the error in linear interpolation on a triangle Error in linear interpolation on a triangle Thomas Sauer (sauer@helena.mi.uni-erlangen.de): computational aspects of multivariate Lagrange interpolation and associated errors (with Yuan Xu) On multivariate Lagrange interpolation Pavel Shvartsman (pshv@math.technion.ac.il): provides a nice proof Yuri Subbotin (yunsub@imm.e-burg.su): dependence of estimates of a multidimensional piecewise polynomial approximation on the geometric characteristics of the triangulation Shayne Waldron (waldron@math.auckland.ac.nz): integral error formula for linear interpolation on a triangle and the corresponding L_p-error bounds The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) Error in linear interpolation on a triangle Thomas Sauer (sauer@helena.mi.uni-erlangen.de): computational aspects of multivariate Lagrange interpolation and associated errors (with Yuan Xu) On multivariate Lagrange interpolation Pavel Shvartsman (pshv@math.technion.ac.il): provides a nice proof Yuri Subbotin (yunsub@imm.e-burg.su): dependence of estimates of a multidimensional piecewise polynomial approximation on the geometric characteristics of the triangulation Shayne Waldron (waldron@math.auckland.ac.nz): integral error formula for linear interpolation on a triangle and the corresponding L_p-error bounds The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) On multivariate Lagrange interpolation Pavel Shvartsman (pshv@math.technion.ac.il): provides a nice proof Yuri Subbotin (yunsub@imm.e-burg.su): dependence of estimates of a multidimensional piecewise polynomial approximation on the geometric characteristics of the triangulation Shayne Waldron (waldron@math.auckland.ac.nz): integral error formula for linear interpolation on a triangle and the corresponding L_p-error bounds The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) Yuri Subbotin (yunsub@imm.e-burg.su): dependence of estimates of a multidimensional piecewise polynomial approximation on the geometric characteristics of the triangulation Shayne Waldron (waldron@math.auckland.ac.nz): integral error formula for linear interpolation on a triangle and the corresponding L_p-error bounds The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) Shayne Waldron (waldron@math.auckland.ac.nz): integral error formula for linear interpolation on a triangle and the corresponding L_p-error bounds The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) The error in linear interpolation at the vertices of a simplex L_p-error bounds and a multivariate form of Hardy's inequality , L_p-error bounds and a multivariate form of Hardy's inequality , Yuan Xu (yuan@bright.uoregon.edu): computational aspects of multivariate Lagrange interpolation and the associated errors (with Sauer) References Some relevant books Linear approximation, A. Sard, AMS monograph (1963) The finite element method for elliptic problems, P. G. Ciarlet (1978) Some older papers which are still of interest Error bounds for linear interpolation on a triangle, J. A. Gregory, In: Mathematics of finite elements and applications (J. Whiteman, ed.) (1975) General Lagrange and Hermite interpolation in R^n with applications to finite element methods, P. G. Ciarlet and P. A. Raviart, Arch. Rational Mech. Anal. 46 (1972), pp 177-199 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 Other sources of information Pages dealing with multivariate polynomial interpolation , Kergin interpolation , and Hermite interpolation Some open problems This document is maintained by Shayne ( waldron@math.auckland.ac.nz ). Last Modified: .

Some relevant books Linear approximation, A. Sard, AMS monograph (1963) The finite element method for elliptic problems, P. G. Ciarlet (1978) Some older papers which are still of interest Error bounds for linear interpolation on a triangle, J. A. Gregory, In: Mathematics of finite elements and applications (J. Whiteman, ed.) (1975) General Lagrange and Hermite interpolation in R^n with applications to finite element methods, P. G. Ciarlet and P. A. Raviart, Arch. Rational Mech. Anal. 46 (1972), pp 177-199 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 Linear approximation, A. Sard, AMS monograph (1963) The finite element method for elliptic problems, P. G. Ciarlet (1978) The finite element method for elliptic problems, P. G. Ciarlet (1978) Some older papers which are still of interest Error bounds for linear interpolation on a triangle, J. A. Gregory, In: Mathematics of finite elements and applications (J. Whiteman, ed.) (1975) General Lagrange and Hermite interpolation in R^n with applications to finite element methods, P. G. Ciarlet and P. A. Raviart, Arch. Rational Mech. Anal. 46 (1972), pp 177-199 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 Error bounds for linear interpolation on a triangle, J. A. Gregory, In: Mathematics of finite elements and applications (J. Whiteman, ed.) (1975) General Lagrange and Hermite interpolation in R^n with applications to finite element methods, P. G. Ciarlet and P. A. Raviart, Arch. Rational Mech. Anal. 46 (1972), pp 177-199 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 General Lagrange and Hermite interpolation in R^n with applications to finite element methods, P. G. Ciarlet and P. A. Raviart, Arch. Rational Mech. Anal. 46 (1972), pp 177-199 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 Sur l'evaluation de l'erreur d'interpolation de Lagrange dans un ouvert de R^n, R. Arcangeli and J. L. Gout, Rev. Francaise Automat. Informat. Rech. Oper., Anal. Numer. 10(3) (1976), pp 5-27 Other sources of information Pages dealing with multivariate polynomial interpolation , Kergin interpolation , and Hermite interpolation Some open problems Some open problems This document is maintained by Shayne ( waldron@math.auckland.ac.nz ). Last Modified: .