TY - JOUR

T1 - On factor width and symmetric H-matrices

AU - Boman, Erik G.

AU - Chen, Doron

AU - Parekh, Ojas

AU - Toledo, Sivan

N1 - Funding Information:
∗ Corresponding author. E-mail addresses: egboman@sandia.gov (E.G. Boman), mycroft@tau.ac.il (D. Chen), ojas@mathcs. emory.edu (O. Parekh), stoledo@tau.ac.il (S. Toledo). 1 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. 2 Supported in part by an IBM Faculty Partnership Award, by grant 572/00 from the Israel Science Foundation (founded by the Israel Academy of Sciences and Humanities), and by grant 2002261 from the United–States–Israel Binational Science Foundation.

PY - 2005/8/1

Y1 - 2005/8/1

N2 - We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric matrices with factor width at most two is exactly the class of (possibly singular) symmetric H-matrices (also known as generalized diagonally dominant matrices) with positive diagonals, H +. We prove bounds on the factor width, including one that is tight for factor widths up to two, and pose several open questions.

AB - We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric matrices with factor width at most two is exactly the class of (possibly singular) symmetric H-matrices (also known as generalized diagonally dominant matrices) with positive diagonals, H +. We prove bounds on the factor width, including one that is tight for factor widths up to two, and pose several open questions.

KW - Combinatorial matrix theory

KW - Factor width

KW - Generalized diagonally dominant

KW - H-matrix

UR - http://www.scopus.com/inward/record.url?scp=21244436473&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2005.03.029

DO - 10.1016/j.laa.2005.03.029

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AN - SCOPUS:21244436473

SN - 0024-3795

VL - 405

SP - 239

EP - 248

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -