Results 31 to 40 of about 539,466 (113)
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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Accurate bidiagonal decomposition of collocation matrices of weighted ϕ‐transformed systems
Numerical Linear Algebra with Applications, 2020 SummaryGiven a system of functions, we introduce the concept of weighted φ‐transformed system, which will include a very large class of useful representations in Statistics and Computer Aided Geometric Design. An accurate bidiagonal decomposition of the collocation matrices of these systems is obtained.
Esmeralda Mainar +2 more
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Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations [PDF]
Applied Mathematics and Computation, 2006 We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A.
Stephen J. Sangwine, Nicolas Le Bihan
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High Relative Accuracy for Corner Cutting Algorithms
AxiomsCorner cutting algorithms are important in computer-aided geometric design and they are associated to stochastic non-singular totally positive matrices. Non-singular totally positive matrices admit a bidiagonal decomposition. For many important examples,
Jorge Ballarín +2 more
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Accurate Computations with Generalized Pascal k-Eliminated Functional Matrices
MathematicsThis paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal k-eliminated functional matrices and Pascal symmetric functional matrices.
Jorge Delgado +2 more
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Bidiagonal factorization of tetradiagonal matrices and Darboux transformations [PDF]
, 2023 Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory.
Mañas Baena, Manuel Enrique +7 more
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Regularization Total Least Squares and Randomized Algorithms
MathematicsIn order to achieve an effective approximation solution for solving discrete ill-conditioned problems, Golub, Hansen, and O’Leary used Tikhonov regularization and the total least squares (TRTLS) method, where the bidiagonal technique is considered to ...
Zhanshan Yang, Xilan Liu, Tiexiang Li
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Totally Positive Wronskian Matrices and Symmetric Functions
AxiomsThe elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matrices
Pablo Díaz +2 more
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Two-way bidiagonalization scheme for downdating the singular-value decomposition
Linear Algebra and its Applications, 1995 Downdating of a matrix means the deletion of an existing row of this matrix. It is shown that the problem of downdating a row in the singular value decomposition of a matrix can be transformed into a problem of bidiagonalizing a diagonal matrix bordered by a column and then diagonalizing this bidiagonal matrix. For the bidiagonalization of a rank-\(r\)
Park, Haesun, Van Huffel, Sabine
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Journal of Mathematical and Fundamental SciencesThis paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries.
Koichi Kondo
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