Structured condition numbers for linear systems with parameterized quasiseparable coefficient matrices Articles uri icon

publication date

  • December 2016

start page

  • 1131

end page

  • 1158

issue

  • 4

volume

  • 73

international standard serial number (ISSN)

  • 1017-1398

electronic international standard serial number (EISSN)

  • 1572-9265

abstract

  • Low-rank structured matrices have attracted much attention in the last decades, since they arise in many applications and all share the fundamental property that can be represented by parameters, where nxn is the size of the matrix. This property has allowed the development of fast algorithms for solving numerically many problems involving low-rank structured matrices by performing operations on the parameters describing the matrices, instead of directly on the matrix entries. Among these problems, the solution of linear systems of equations is probably the most basic and relevant one.

keywords

  • condition numbers; linear systems; low-rank structured matrices; quasiseparable matrices; quasiseparable representation; givens-vector representation; inversion algorithms; solvers