Results 11 to 20 of about 539,466 (113)
Accurate bidiagonal decomposition of Lagrange–Vandermonde matrices and applications [PDF]
Numerical Linear Algebra with Applications, 2023 AbstractLagrange–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 ...
Marco García, Ana +2 more
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A tensor bidiagonalization method for higher‐order singular value decomposition with applications
Numerical Linear Algebra with Applications, 2023 AbstractThe 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 presented.
Abderrahmane El Hachimi +3 more
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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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Bidiagonal decompositions and total positivity of some special matrices [PDF]
Operators and Matrices, 2022 The article contains 15 pages.
Grover, Priyanka, Panwar, Veer Singh
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Bidiagonal decompositions of oscillating systems of vectors [PDF]
Linear Algebra and its Applications, 2008 The authors obtain necessary and sufficient conditions for a matrix \(V\) to be a matrix of eigenvectors of a totally positive matrix. Namely, this is the case if and only if \(V\) and \(V^{-T}\) are lowerly totally positive. These conditions translate into easy requirements on the parameters in the bidiagonal decompositions of \(V\) and \(V^{-T}\). By
Dopico, Froilán M., Koev, Plamen
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Bidiagonal Decompositions and Accurate Computations for the Ballot Table and the Fibonacci Matrix
Numerical Linear Algebra with ApplicationsABSTRACT Riordan arrays include many important examples of matrices. Here we consider the ballot table and the Fibonacci matrix. For finite truncations of these Riordan arrays, we obtain bidiagonal decompositions. Using them, algorithms to solve key linear algebra problems for ballot tables and Fibonacci matrices with high relative ...
Jorge Ballarín +2 more
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Bidiagonal Decompositions and High‐Accuracy Computations for Newton Collocation Matrices
Numerical Linear Algebra with ApplicationsABSTRACT We consider a class of collocation matrices associated with the Newton basis of the space of polynomials of degree at most , evaluated at a set of nodes. In the most general setting, we allow of these nodes to either coincide with or differ from those defining the Newton basis.
E. Mainar, A. Marco, B. Rubio, R. Viaña
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Accurate bidiagonal decomposition of totally positive Cauchy–Vandermonde matrices and applications [PDF]
Linear Algebra and its Applications, 2017 Cauchy–Vandermonde matrices play a fundamental role in rational interpolation theory and in other fields. When all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings, these matrices are totally positive.
Marco, Ana +2 more
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A Robust Image Watermarking Scheme Using Z-Transform, Discrete Wavelet Transform and Bidiagonal Singular Value Decomposition [PDF]
Computers, Materials & Continua, 2019 Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images, videos, and audio data. Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.
N. Jayashree, R. S. Bhuvaneswaran
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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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