Abstract
The authors discuss the solution of sparse linear equations Kd = r, where K is a symmetric and specially structured indefinite matrix that often arises in numerical optimization. For such K, the indefinite factorization K = LDL{sup T} is known to exist in exact arithmetic with 1 {times} 1 pivots and no row or column interchanges. It is shown that the stability of the LDL{sup T} factorization of this matrix is naturally connected with the stability of the LDM{sup T} factorization of a closely related unsymmetric positive-definite matrix. Conditions are given that allow the stable numerical solution of this system by Gaussian elimination without row and column interchanges.
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.
