Abstract For X, Y ∈ M n,m , it is said that X g-tridiagonal majorized by (and denoted ≺ gt ) if there exists a tridiagonal g-doubly stochastic matrix A such = AY . In this paper, the linear preservers and strong of are characterized on

If is the computed solution to a tridiagonal system Ax b obtained by Gaussian elimination, what is the "best" bound available for the error x and how can it be computed efficiently? This question is answered using backward error analysis, perturbation theory, and properties of the LU factorization of A. For three practically important classes of tridiagonal matrix, those that are symmetric posi...

A numerical method for computing the logarithm of a symmetric positive dee-nite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad e approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite eecient when th...

The orthogonal qd algorithm with shifts (oqds algorithm), proposed by von Matt, is an algorithm for computing the singular values of bidiagonal matrices. This algorithm is accurate in terms of relative error, and it is also applicable to general triangular matrices. In particular, for lower tridiagonal matrices, BLAS Level 2.5 routines are available in preprocessing stage for this algorithm. BL...

In this article the unitary equivalence transformation of normal matrices to tridiagonal form is studied. It is well-known that any matrix is unitarily equivalent to a tridiagonal matrix. In case of a normal matrix the resulting tridiagonal inherits a strong relation between its superand subdiagonal elements. The corresponding elements of the superand subdiagonal will have the same absolute val...

Abstract. This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity. If the bl...

The recent emergence of the discrete fractional Fourier transform (DFRFT) has caused a revived interest in the eigenanalysis of the discrete Fourier transform (DFT) matrix F with the objective of generating orthonormal Hermite-Gaussian-like eigenvectors. The Grünbaum tridiagonal matrix T – which commutes with matrix F – has only one repeated eigenvalue with multiplicity two and simple remaining...

In this paper, computational efficient technique is proposed to calculate the eigenvalues of a tridiagonal system matrix using Strum sequence and Gerschgorin theorem. The proposed technique is applicable in various control system and computer engineering applications. KeywordsEigenvalues, tridiagonal matrix, Strum sequence and Gerschgorin theorem. I.INTRODUCTION Solving tridiagonal linear syste...

We call these equations the Donaldson-Thomas equations, and a solution (A,u) to these equations Donaldson-Thomas instanton. In [Ta1], we studied local structures of the moduli space of the DonaldsonThomas instantons such as the infinitesimal deformation and the Kuranishi map of the moduli space. In this article, we prove a weak compactness theorem of the Donaldson-Thomas instantons. This descri...

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block-tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which freq...