On the Lanczos Method for Computing Some Matrix Functions

The study of matrix functions is highly significant and has important applications in control theory, quantum mechanics, signal processing, and machine learning. Previous work has mainly focused on how to use the Krylov-type method to efficiently calculate matrix functions f(A)β and βTf(A)β when A i...

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Bibliographic Details
Published inAxioms Vol. 13; no. 11; p. 764
Main Authors Gu, Ying, Srivastava, Hari Mohan, Liu, Xiaolan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2024
Subjects
Approximation
Chebyshev polynomial
Control theory
Decomposition
Krylov subspace
Lanczos method
Legendre polynomial
Machine learning
matrix logarithm function
Methods
Polynomials
Quantum mechanics
United States
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ISSN2075-1680
2075-1680
DOI10.3390/axioms13110764

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Summary:The study of matrix functions is highly significant and has important applications in control theory, quantum mechanics, signal processing, and machine learning. Previous work has mainly focused on how to use the Krylov-type method to efficiently calculate matrix functions f(A)β and βTf(A)β when A is symmetric. In this paper, we mainly illustrate the convergence using the polynomial approximation theory for the case where A is symmetric positive definite. Numerical results illustrate the effectiveness of our theoretical results.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13110764