The Strong Stability of Algorithms for Solving Symmetric Linear Systems
James R. Bunch, W. James Demmel, Charles F. Van Loan · SIAM Journal on Matrix Analysis and Applications · 1989
An algorithm for solving linear equations is stable on the class of nonsingular symmetric matrices or on the class of symmetric positive definite matrices if the computed solution solves a system that is near the original problem. Here it is shown that any stable algorithm is also strongly stable on the same matrix class if the computed solution solves a nearby problem that is also symmetric or symmetric positive definite.