Parallel homotopy algorithm for symmetric large sparse eigenproblems (Q1900754)

The homotopy method is applied to solve the eigenproblem \(Ax= \lambda x\) for real symmetric large sparse matrices \(A\). That is, a simpler nearby matrix \(D\) is introduced and its eigenpairs are continuously mapped to those of \(A\). The problem of choosing an appropriate starting matrix \(D\) as well as regularity and bifurcation issues for \(\lambda(t)\) and \(x(t)\) are discussed. A parallel homotopy algorithm is presented and its performance is compared to that of the Lanczos algorithm.