Total positivity and accurate computations with Gram matrices of Bernstein bases

In this paper, an accurate method to construct the bidiagonal factorization of Gram (mass) matrices of Bernstein bases of positive and negative degree is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. Numerical examples are included.

Saved in:
Bibliographic Details
Published inNumerical algorithms Vol. 91; no. 2; pp. 841 - 859
Main Authors Mainar, E., Peña, J. M., Rubio, B.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2022
Springer Nature B.V
Subjects
Accuracy
Algebra
Algorithms
Approximation
Computer Science
Decomposition
Eigenvalues
Linear algebra
Linear equations
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Polynomials
Theory of Computation
Gram matrices
Totally positive matrices
Bidiagonal decompositions
High relative accuracy
Bernstein bases
Online AccessGet full text

Cover

More Information
Summary:In this paper, an accurate method to construct the bidiagonal factorization of Gram (mass) matrices of Bernstein bases of positive and negative degree is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. Numerical examples are included.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01284-0