Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal properties of tensor product of B-bases

Jorge Delgado, Héctor Orera, Juan Manuel Peña

Abstract

It is proved the optimal conditioning for the infinity norm of collocation matrices of the tensor product of normalized B-bases among the tensor product of all normalized totally positive bases of the corresponding space of functions. Bounds for the minimal eigenvalue and singular value and illustrative numerical examples are also included.

Optimal properties of tensor product of B-bases

Abstract

It is proved the optimal conditioning for the infinity norm of collocation matrices of the tensor product of normalized B-bases among the tensor product of all normalized totally positive bases of the corresponding space of functions. Bounds for the minimal eigenvalue and singular value and illustrative numerical examples are also included.
Paper Structure (2 sections, 1 theorem, 6 equations, 4 tables)

This paper contains 2 sections, 1 theorem, 6 equations, 4 tables.

Table of Contents

  1. Introduction and main results
  2. Numerical tests

Key Result

Theorem 1

Let $u^1=(u_0^1,\ldots,u_m^1)$ be an NTP basis on $[a,b]$ of a space of functions $\mathcal{U}_1$, $u^2=(u_0^2,\ldots,u_n^2)$ be an NTP basis on $[c,d]$ of a space of functions $\mathcal{U}_2$ and let $v^1=(v_0^1,\ldots,v_m^1)$ and $v^2=(v_0^2,\ldots,v_n^2)$ be the normalized B-bases of $\mathcal{U}

Theorems & Definitions (2)

  • Theorem 1
  • proof