Numerical Methods for Solving Large Sparse Eigenvalue Problems and for theAnalysis of Bifurcation Phenomena

摘要

Research was concerned with designing and analyzing efficient and novel iterativealgorithms for solving large sparse linear systems, typically arising from the discretizations of partial differential equations, which are highly parallelizable and converge fast. These include domain decomposition algorithms and multilevel preconditioners. Some basic dense linear algebra problems, including rank-revealing QR factorizations and stable Toeplitz solvers, which have applications to signal processing were considered.