AxiomsThe approach to solving linear systems with structured matrices by means of the bidiagonal factorization of the inverse of the coefficient matrix is first considered in this review article, the starting point being the classical Björck–Pereyra algorithms
Jose-Javier Martinez
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Bidiagonal Factorizations of Filbert and Lilbert Matrices [PDF]
AxiomsExtensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices.
Beatriz Rubio-Serrano +2 more
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Positive bidiagonal factorization of tetradiagonal Hessenberg matrices [PDF]
Linear Algebra and Its Applications, 2023 Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. In this paper conditions, in terms of continued fractions, for an oscillatory tetradiagonal Hessenberg matrix to have such positive bidiagonal factorization are found.
Manuel Manas
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Bidiagonal factorization of tetradiagonal matrices and Darboux transformations [PDF]
Analysis and Mathematical Physics, 2023 AbstractRecently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima–Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi–Piñeiro multiple orthogonal polynomials are discussed at the light of ...
Manuel Manas +2 more
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Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials [PDF]
Advances in Mathematics, 2023 33 ...
Manuel Manas
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Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization [PDF]
Linear Algebra and Its Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jürgen Garloff +2 more
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Accurate bidiagonal factorization of quantum Hilbert matrices [PDF]
Linear Algebra and Its Applications, 2023 A bidiagonal decomposition of quantum Hilbert matrices is obtained and the total positivity of these matrices is proved. This factorization is used to get accurate algebraic computations with these matrices. The numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed.
Beatriz Rubio-Serrano +2 more
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A test and bidiagonal factorization for certain sign regular matrices
Linear Algebra and Its Applications, 2013 This paper deals with bidiagonal factorization and tests for sign regular matrices. The author obtains a characterization of sign regular matrices with signature \(\epsilon=(1,1,\hdots,1,-1)\) using a reduced numbers of minors. This is used to improve the characterizations of the well-known approach for totally nonnegative matrices. Furthermore, a test
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Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials
Linear Algebra and Its Applications14 pages, 2 ...
A Foulquié Moreno, Manuel Manas
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Sparse Matrix Based Low-Complexity, Recursive, and Radix-2 Algorithms for Discrete Sine Transforms
IEEE Access, 2021 This paper presents factorizations of each discrete sine transform (DST) matrix of types I, II, III, and IV into a product of sparse, diagonal, bidiagonal, and scaled orthogonal matrices.
Sirani M. Perera, Levi E. Lingsch
doaj +1 more source