Solution of bordered singular systems in numerical continuation and bifurcation
Linear systems with coefficient matrices in block form \(M=\left({A\atop C^ T}{B\atop D}\right)\) are considered in situations, where a specialized solver can be used for \(A\) (for example, if \(A\) is sparse, banded, etc.) but where \(C^ T\), \(B\) and \(D\) are dense. The author considers the additional difficulty of \(A\) being nearly singular and thus ill-conditioned. Numerical tests are described using the mixed block elimination method of the author and \textit{J. D. Pryce} [IMA J. Numer. Anal. 13, No. 2, 161-180 (1993; Zbl 0778.65017)]. The tests indicate that such linear systems can be solved in a stable way even if a black-box solver is used for the nearly singular matrix.
scientific article; zbMATH DE number 643765
scientific article