This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise TLSE are derived. Computable expressions upper bounds these also given avoid costly Kronecker product-based operations. The results unify ones TLS problem. For problems equilibratory input data, n...

The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this paper, we present a block Lanczos method for tridiagonalizing complex symmetric matrices. Also, we propose a novel componentwise technique for detecting the loss of orthogonality to stablize the block ...

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approximation coupled with scaling and squaring is used to compute the exponential of an essentially nonnegative matrix. An a priori componentwise r...

Let S = K[x1, . . . , xn] be a polynomial ring and R = S/I be a graded K-algebra where I ⊂ S is a graded ideal. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S. We prove the conjecture in the case that codim(R) = 2 which generalizes results in [10] and [13]. We also g...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and He...

This paper is concerned with the problem of verifying the accuracy of an approximate solution of a sparse linear system whose coefficient matrix is an H-matrix. Fast and efficient methods of calculating componentwise error bounds of the computed solution are proposed. The methods are based on the verified criterion for an M-matrix. The main point of this article is that the proposed methods can...