Componentwise error analysis for linear systems associated with sign regular matrices

摘要

In this paper, we present a componentwise error analysis of solving linear systems whose coefficient matrices are sign regular matrices with the same signature sequences as those of Jacobi sign regular matrices associated with corner cutting algorithms in computer aided geometric design. It is interesting to show that for such sign regular matrices, in finite precision floating point arithmetic, the computed factors by Gaussian elimination with the last two row exchanges satisfy a small componentwise relative backward error. Consequently, the computed solutions of linear systems associated with such matrices admit pleasantly small componentwise relative backward errors.