Year-end Sale % OFF 
Abstract
We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to the simpler block GMRES method. Moreover, it is shown that the residual-based method is numerically more stable than the simpler block GMRES method. Based on the deflation strategy proposed by Calandra et al. (2013), we derive a deflation strategy to detect the possible linear dependence of the residuals and a near rank deficiency occurring in the block Arnoldi procedure. Numerical experiments are conducted to illustrate the performance of the new method.
Highlights
IntroductionIn the block Arnoldi algorithm, YiTYi = I holds due to the QR factorizations, and YiTYj = 0 when i ≠ j, where I is a unit matrix and 0 is a zero matrix of order s
In this paper, we consider iterative methods for solving a system of linear algebraic equations: AX = B, (1)where A is a nonsingular matrix of order n and X = [x1, . . . , xs] and B = [b1, . . . , bs] are rectangular matrices of dimension n×s with s ≤ n
Calandra et al derived a deflation strategy to detect a near rank deficiency occurring in the block Arnoldi procedure in [7]
Summary
In the block Arnoldi algorithm, YiTYi = I holds due to the QR factorizations, and YiTYj = 0 when i ≠ j, where I is a unit matrix and 0 is a zero matrix of order s. This indicates that the whole process is equivalent to the one in which the block vectors are generated column by column using an ordinary modified Gram-Schmidt process. The block GMRES method with deflation at each iteration was proposed in [6]. We call this case the residual-based simpler block GMRES
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
