TY - JOUR
T1 - Semi Inherited Bivariate Interpolation
AU - Mohammad Ali Fariborzi Araghi & Amir Fallahzadeh
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 - <p style="text-align: justify;">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.</p>