Results 21 to 30 of about 475,064 (272)
A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers [PDF]
Mathematics, 2019 In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit ...
Yunlan Wei +3 more
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On a family of tridiagonal matrices
, 2008 We show that certain integral positive definite symmetric tridiagonal matrices of determinant $n$ are in one to one correspondence with elements of $(\mathbb Z/n\mathbb Z)^*$. We study some properties of this correspondence. In a somewhat unrelated second part we discuss a construction which associates a sequence of integral polytopes to every integral
Roland Bacher
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On twisted factorizations of block tridiagonal matrices
Procedia Computer Science, 2010 AbstractNon-symmetric and symmetric twisted block factorizations of block tridiagonal matrices are discussed. In contrast to non-blocked factorizations of this type, localized pivoting strategies can be integrated which improves numerical stability without causing any extra fill-in.
Wilfried N. Gansterer, Gerhard König
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Bidiagonalization of (k, k + 1)-tridiagonal matrices
Special Matrices, 2019 In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix ...
Takahira S., Sogabe T., Usuda T.S.
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Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations.
J Comput Appl Math, 2012 König G, Moldaschl M, Gansterer WN.
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On the spectrum of tridiagonal matrices with two-periodic main diagonal [PDF]
Special MatricesWe find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal. This is expressed in terms of the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main ...
Dyachenko Alexander, Tyaglov Mikhail
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On Computing Eigenvectors of Symmetric Tridiagonal Matrices
Structured Matrices in Numerical Linear Algebra, 2019 The computation of the eigenvalue decomposition of symmetric matrices is one of the most investigated problems in numerical linear algebra. For a matrix of moderate size, the customary procedure is to reduce it to a symmetric tridiagonal one by means of an orthogonal similarity transformation and then compute the eigendecomposition of the tridiagonal ...
Mastronardi, Nicola +2 more
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Tridiagonalizing random matrices
Physical Review D, 2023 The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, the main goal of random matrix theory (RMT) has been to derive the eigenvalue statistics of matrices drawn from a given distribution.
Vijay Balasubramanian +2 more
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A Fast Algorithm for the Eigenvalue Bounds of a Class of Symmetric Tridiagonal Interval Matrices
AppliedMath, 2023 The eigenvalue bounds of interval matrices are often required in some mechanical and engineering fields. In this paper, we improve the theoretical results presented in a previous paper “A property of eigenvalue bounds for a class of symmetric tridiagonal
Quan Yuan, Zhixin Yang
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Relation between determinants of tridiagonal and certain pentadiagonal matrices [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2014 Jolanta Borowska, Lena Łacińska
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