Results 11 to 20 of about 62,500 (93)
Bidiagonal factorizations and quasi-oscillatory rectangular matrices [PDF]
Linear Algebra and its Applications, 2008 An \(m\times n\) real matrix \(A\) is called totally nonnegative if all its minors are nonnegative, and totally positive if all its minors are positive. The authors define a totally nonnegative matrix \(A\) to be quasi-oscillatory if some positive integral power of \(AA^{\top}\) is totally positive.
Gassó, Maria T., Torregrosa, Juan R.
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Bidiagonal factorizations with some parameters equal to zero [PDF]
Linear Algebra and its Applications, 2011 This paper deals with the bidiagonal factorization of complex matrices. By the means of the new concepts of relevant submatrix and almost totally nonsingular matrix, necessary and sufficient conditions are obtained for a nonsingular matrix to have a bidiagonal factorization with some parameters of the subdiagonal (or superdiagonal) being equal to zero.
Huang, Rong, Liu, Jianzhou
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Elementary bidiagonal factorizations [PDF]
Linear Algebra and its Applications, 1999 An elementary bidiagonal matrix is a square matrix such that every entry in the diagonal is \(1,\) exactly one entry either on the sub- or superdiagonal is nonzero, and all other entries are zero. The authors show that every \(n\times n\) matrix is a product of elementary bidiagonal matrices. For special cases, e.g., for \(2\times 2\) and \(3\times 3\)
Johnson, Charles R. +2 more
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Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality [PDF]
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Branquinho, Amílcar +4 more
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Green Matrices, Minors and Hadamard Products
Axioms, 2023 Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations.
Jorge Delgado +2 more
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On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
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Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials [PDF]
, 2023 This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ${}_3F_2$ and is proven ...
Mañas, Manuel +3 more
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Total positivity and accurate computations with Gram matrices of Said‐Ball bases
Numerical Linear Algebra with Applications, Volume 30, Issue 6, December 2023., 2023 Abstract In this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained.
E. Mainar, J. M. Peña, B. Rubio
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Journal of Chemometrics, Volume 37, Issue 10, October 2023., 2023 Abstract In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR) may often provide efficient low‐dimensional model solutions. In unsupervised situations, the same may be true for principal component analysis (PCA).
Joakim Skogholt +4 more
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Inexact inner–outer Golub–Kahan bidiagonalization method: A relaxation strategy
Numerical Linear Algebra with Applications, Volume 30, Issue 5, October 2023., 2023 Abstract We study an inexact inner–outer generalized Golub–Kahan algorithm for the solution of saddle‐point problems with a two‐times‐two block structure. In each outer iteration, an inner system has to be solved which in theory has to be done exactly. Whenever the system is getting large, an inner exact solver is, however, no longer efficient or even ...
Vincent Darrigrand +3 more
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