Volume 27, Issue 2
Semi Inherited Bivariate Interpolation

Anal. Theory Appl., 27 (2011), pp. 138-149.

Published online: 2011-04

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• Abstract

The bivariate interpolation in two dimensional space $\mathbf{R}^2$ is more complicated than that in one dimensional space $\mathbf{R}$, because there is no Haar space of continuous functions in $\mathbf{R}^2$. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization.

• AMS Subject Headings

15A23, 65F05, 65D05

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@Article{ATA-27-138, author = {}, title = {Semi Inherited Bivariate Interpolation}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {2}, pages = {138--149}, abstract = {

The bivariate interpolation in two dimensional space $\mathbf{R}^2$ is more complicated than that in one dimensional space $\mathbf{R}$, because there is no Haar space of continuous functions in $\mathbf{R}^2$. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0138-z}, url = {http://global-sci.org/intro/article_detail/ata/4587.html} }
TY - JOUR T1 - Semi Inherited Bivariate Interpolation JO - Analysis in Theory and Applications VL - 2 SP - 138 EP - 149 PY - 2011 DA - 2011/04 SN - 27 DO - http://doi.org/10.1007/s10496-011-0138-z UR - https://global-sci.org/intro/article_detail/ata/4587.html KW - inherited factorization, inherited interpolation, semi inherited interpolation, bivariate interpolation, interpolation matrix. AB -

The bivariate interpolation in two dimensional space $\mathbf{R}^2$ is more complicated than that in one dimensional space $\mathbf{R}$, because there is no Haar space of continuous functions in $\mathbf{R}^2$. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization.

Mohammad Ali Fariborzi Araghi & Amir Fallahzadeh. (1970). Semi Inherited Bivariate Interpolation. Analysis in Theory and Applications. 27 (2). 138-149. doi:10.1007/s10496-011-0138-z
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