Efficient solution of A, x (k) =b (k) using A -1

Adi Ditkowski*, Gadi Fibich, Nir Gavish

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this work, we consider the problem of solving x (k) =b (k), k= 1,...K,where b (k+1) = f(x (k)). We show that when A is a full n × n matrix and K ≥cn, where c≦ 1 depends on the specific software and hardware setup, it is faster to solve Ax (k) =b (k) for k = 1,...K by explicitly evaluating the inverse matrix A -1 rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.

Original languageEnglish
Pages (from-to)29-44
Number of pages16
JournalJournal of Scientific Computing
Volume32
Issue number1
DOIs
StatePublished - Jul 2007

Keywords

  • Linear systems
  • Matrix inversion

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