TY - JOUR
T1 - On multivariate interpolation by generalized polynomials on subsets of grids
AU - MÃ¼hlbach, G.
PY - 1988/9
Y1 - 1988/9
N2 - This note may be regarded as a complement to a paper of H. Werner [17] who has carried over Newton's classical interpolation formula to Hermite interpolation by algebraic polynomials of several real variables on certain subsets of grids. Here generalized polynomials of several real or complex variables are treated. Recursive procedures are presented showing that interpolation by generalized multivariate polynomials is performed nearly as simply as interpolation by algebraic polynomials. Having in general the same approximation power, generalized polynomials may be better adapted to special situations. In particular, the results of this note can be used for constructing nonpolynomial finite elements since in that case the interpolation points usually are rather regular subsystems of grids. Though the frame is more general than in [17] some of our proofs are simpler. As an alternative method to evaluate multivariate generalized interpolation polynomials for rectangular grids a Neville-Aitken algorithm is presented.
AB - This note may be regarded as a complement to a paper of H. Werner [17] who has carried over Newton's classical interpolation formula to Hermite interpolation by algebraic polynomials of several real variables on certain subsets of grids. Here generalized polynomials of several real or complex variables are treated. Recursive procedures are presented showing that interpolation by generalized multivariate polynomials is performed nearly as simply as interpolation by algebraic polynomials. Having in general the same approximation power, generalized polynomials may be better adapted to special situations. In particular, the results of this note can be used for constructing nonpolynomial finite elements since in that case the interpolation points usually are rather regular subsystems of grids. Though the frame is more general than in [17] some of our proofs are simpler. As an alternative method to evaluate multivariate generalized interpolation polynomials for rectangular grids a Neville-Aitken algorithm is presented.
KW - AMS Subject Classifications: 65D05, 41A05
KW - multivariate generalized divided differences
KW - multivariate generalized polynomials
KW - Multivariate Hermite interpolation
UR - http://www.scopus.com/inward/record.url?scp=0023831841&partnerID=8YFLogxK
U2 - 10.1007/BF02251249
DO - 10.1007/BF02251249
M3 - Article
AN - SCOPUS:0023831841
VL - 40
SP - 201
EP - 215
JO - Computing
JF - Computing
SN - 0010-485X
IS - 3
ER -