Results 21 to 30 of about 1,086 (62)
Bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math.
He Jun +4 more
doaj +1 more source
Shrinkage Function And Its Applications In Matrix Approximation
, 2017 The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are
Boas, Toby +4 more
core +1 more source
Computing the smallest singular triplets of a large matrix
Results in Applied Mathematics, 2019 In this paper we present a new type of restarted Krylov methods for calculating the smallest singular triplets of a large sparse matrix, A. The new framework avoids the Lanczos bidiagonalization process and the use of polynomial filtering.
Achiya Dax
doaj +1 more source
THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM
Forum of Mathematics, Sigma, 2015 The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit Courant–Fischer type min–max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić.
XIN LIANG, REN-CANG LI
doaj +1 more source
Variable-step finite difference schemes for the solution of Sturm-Liouville problems
, 2014 We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.
Amodio, Pierluigi, Settanni, Giuseppina
core +1 more source
The Anderson model of localization: a challenge for modern eigenvalue methods [PDF]
, 1997 We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real ...
Elsner, U. +4 more
core +4 more sources
The smallest singular value anomaly: The reasons behind sharp anomaly
Special MatricesLet AA be an arbitrary matrix in which the number of rows, mm, is considerably larger than the number of columns, nn. Let the submatrix Ai,i=1,…,m{A}_{i},\hspace{0.33em}i=1,\ldots ,m, be composed from the first ii rows of AA, and let βi{\beta }_{i ...
Dax Achiya
doaj +1 more source
Block diagonalization of (p, q)-tridiagonal matrices
Special MatricesIn this article, we study the block diagonalization of (p,q)\left(p,q)-tridiagonal matrices and derive closed-form expressions for the number and structure of diagonal blocks as functions of the parameters pp, qq, and nn. This reduction enables efficient
Manjunath Hariprasad
doaj +1 more source
M-tensors and The Positive Definiteness of a Multivariate Form [PDF]
, 2012 We study M-tensors and various properties of M-tensors are given. Specially, we show that the smallest real eigenvalue of M-tensor is positive corresponding to a nonnegative eigenvector.
Qi, Liqun, Zhang, Liping, Zhou, Guanglu
core
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.
doaj +1 more source