Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization.
Algebraic properties of the block GMRES and block Arnoldi methods.
Oblique projection methods for linear systems with multiple right-hand sides.
A block version of BiCGSTAB for linear systems with multiple right-hand sides.
A breakdown-free Lanczos type algorithm for solving linear systems.
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....
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