Matrix analysis
Topics in matrix analysis
Bounding the error in Gaussian Elimination for Tridiagonal systems
SIAM Journal on Matrix Analysis and Applications
Convexity of rational curves and total positivity
Journal of Computational and Applied Mathematics
Linear Systems
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
International Journal of Systems Science
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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.