Title: A small note on the scaling of symmetric positive definite semiseparable matrices
Authors: Vandebril, Raf
Golub, Gene H
Van Barel, Marc
Issue Date: Dec-2004
Publisher: Stanford's Scientific Computing and Computational Mathematics Program (SCCM)
Abstract: In this paper we will adapt a known method for diagonal scaling of symmetric positive definite
tridiagonal matrices towards the semiseparable case. Based on the fact that a symmetric, positive definite
tridiagonal matrix T satisfies property A, one can easily construct a diagonal matrix ˆ
D such that DTD
has the lowest condition number over all matrices DT D, for any choice of diagonal matrix D. Knowing
that semiseparable matrices are the inverses of tridiagonal matrices, one can derive similar properties for
semiseparable matrices. Here, we will construct the optimal diagonal scaling of a semiseparable matrix,
based on a new inversion formula for semiseparable matrices.
Three types of numerical experiments are performed. In a first experiment we compare the condition
numbers of the semiseparable matrices before and after the scaling. In a second experiment we use the
diagonal scaling for solving linear systems, and compare the results with and without scaling. In the
final experiment some special semiseparable matrices, arrising in statistical applications are used for the
scaling procedure.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section

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