Total positivity and accurate computations with Gram matrices of Bernstein bases

被引：0
|
作者：
E. Mainar
J. M. Peña
B. Rubio
机构：
[1] Universidad de Zaragoza,Departamento de Matemática Aplicada/IUMA
来源：
Numerical Algorithms | 2022年 / 91卷
关键词：
High relative accuracy; Bidiagonal decompositions; Totally positive matrices; Gram matrices; Bernstein bases;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：841 / 859
页数：18
相关论文
共 50 条
  • [1] Total positivity and accurate computations with Gram matrices of Bernstein bases
    Mainar, E.
    Pena, J. M.
    Rubio, B.
    NUMERICAL ALGORITHMS, 2022, 91 (02) : 841 - 859
  • [2] Total positivity and accurate computations with Gram matrices of Said-Ball bases
    Mainar, E.
    Pena, J. M.
    Rubio, B.
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2023, 30 (06)
  • [3] On the total positivity of q-Bernstein mass matrices and their accurate computations
    Mainar, E.
    Pena, J. M.
    Rubio, B.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 451
  • [4] Accurate and efficient computations with Wronskian matrices of Bernstein and related bases
    Mainar, Esmeralda
    Pena, Juan M.
    Rubio, Beatriz
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2022, 29 (03)
  • [5] Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases
    E. Mainar
    J. M. Peña
    B. Rubio
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
  • [6] Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases
    Mainar, E.
    Pena, J. M.
    Rubio, B.
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (03)
  • [7] On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
    Mainar, Esmeralda
    Pena, Juan Manuel
    Rubio, Beatriz
    AXIOMS, 2023, 12 (09)
  • [8] Accurate computations with collocation matrices of rational bases
    Delgado, J.
    Pena, J. M.
    APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (09) : 4354 - 4364
  • [9] ACCURATE COMPUTATIONS WITH TOTALLY POSITIVE BERNSTEIN-VANDERMONDE MATRICES
    Marco, Ana
    Martinez, Jose-Javier
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2013, 26 : 357 - 380
  • [10] ACCURATE COMPUTATIONS WITH COLLOCATION MATRICES OF q-BERNSTEIN POLYNOMIALS
    Delgado, Jorge
    Pena, J. M.
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (02) : 880 - 893
12345