Results 11 to 20 of about 34,257 (101)
Bidiagonal decompositions, minors and applications
The Electronic Journal of Linear Algebra, 2012 Matrices, called e-BD matrices, that have a bidiagonal decomposition satisfying some sign constraints are analyzed. The e-BD matrices include all nonsingular totally positive matrices, as well as their matrices opposite in sign and their inverses. The signs of minors of e-BD matrices are analyzed. The zero patterns of e-BD matrices and their triangular
A. Barreras, J. Pena
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Accurate bidiagonal decomposition of Lagrange–Vandermonde matrices and applications
Numerical Linear Algebra with Applications, Volume 31, Issue 1, January 2024., 2023 Abstract Lagrange–Vandermonde matrices are the collocation matrices corresponding to Lagrange‐type bases, obtained by removing the denominators from each element of a Lagrange basis. It is proved that, provided the nodes required to create the Lagrange‐type basis and the corresponding collocation matrix are properly ordered, such matrices are strictly ...
Ana Marco +2 more
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A tensor bidiagonalization method for higher‐order singular value decomposition with applications
Numerical Linear Algebra with Applications, Volume 31, Issue 2, March 2024., 2023 Abstract The need to know a few singular triplets associated with the largest singular values of a third‐order tensor arises in data compression and extraction. This paper describes a new method for their computation using the t‐product. Methods for determining a couple of singular triplets associated with the smallest singular values also are ...
A. El Hachimi +3 more
wiley +6 more sources
Accurate bidiagonal decomposition and computations with generalized Pascal matrices
Journal of Computational and Applied Mathematics, 2021 This paper provides an accurate method to obtain the bidiagonal factorization of many generalized Pascal matrices, which in turn can be used to compute with high relative accuracy the eigenvalues, singular values and inverses of these matrices. Numerical examples are included.
Jorge Delgado 0001 +2 more
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The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics [PDF]
SIAM Journal on Numerical Analysis, 1991 The authors present an algorithm to compute the singular value decomposition of a bidiagonal matrix \(B\) with an error bound depending on the relative gap. It is also shown that this algorithm computes the singular vectors as well as singular values to this accuracy.
Deift, Percy +3 more
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Positive bidiagonal factorization of tetradiagonal Hessenberg matrices [PDF]
, 2023 2023 Acuerdos transformativos CRUERecently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions,
Mañas Baena, Manuel Enrique +7 more
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The Power of Bidiagonal Matrices [PDF]
, 2023 Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices.
Higham, Nicholas J.
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Circular bidiagonal pairs [PDF]
, 2022 A square matrix is said to be circular bidiagonal whenever (i) each nonzero entry is on the diagonal, or the subdiagonal, or in the top-right corner; (ii) each subdiagonal entry is nonzero, and the entry in the top-right corner is nonzero. Let $\mathbb F$
Žitnik, Arjana, Terwilliger, Paul
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Bidiagonal decomposition of totally positive Bernstein‐Vandermonde matrices [PDF]
PAMM, 2007 AbstractThe class of Bernstein‐Vandermonde matrices (a generalization of Vandermonde matrices arising when the monomial basis is replaced by the Bernstein basis) is considered. A convenient ordering of their rows makes these matrices strictly totally positive.
José‐Javier Martínez, Ana Marco
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Hessenberg, Tridiagonal And Bidiagonal Decomposition
, 2023 Tema ovoga rada su matrice i različite dekompozicije matrica. Dekompozicija matrica je postupak kojim se složena matrica razvija kao produkt više složenih matrica kako bi se olakšala analiza ili rješavanje matematičkih problema.
Dujček, Mateja
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