## Details

Original language | English |
---|---|

Pages (from-to) | 201-215 |

Number of pages | 15 |

Journal | Computing |

Volume | 40 |

Issue number | 3 |

Publication status | Published - Sept 1988 |

## Abstract

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.

## Keywords

- AMS Subject Classifications: 65D05, 41A05, multivariate generalized divided differences, multivariate generalized polynomials, Multivariate Hermite interpolation

## ASJC Scopus subject areas

- Computer Science(all)
**Software**- Mathematics(all)
**Theoretical Computer Science**- Mathematics(all)
**Numerical Analysis**- Computer Science(all)
**Computer Science Applications**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**

## Cite this

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**On multivariate interpolation by generalized polynomials on subsets of grids.**/ Mühlbach, G.

In: Computing, Vol. 40, No. 3, 09.1988, p. 201-215.

Research output: Contribution to journal › Article › Research › peer review

*Computing*, vol. 40, no. 3, pp. 201-215. https://doi.org/10.1007/BF02251249

*Computing*,

*40*(3), 201-215. https://doi.org/10.1007/BF02251249

}

TY - JOUR

T1 - On multivariate interpolation by generalized polynomials on subsets of grids

AU - Mühlbach, 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 -