How Orthogonality is Lost in Krylov Methods
In this paper we examine the behaviour of finite precision Krylov methods for the algebraic eigenproblem. Our approach presupposes only some basic knowledge in linear algebra and may serve as a basis for the examination of a wide variety of Krylov methods. The analysis carried out does not yield exact bounds on the accuracy of Ritz values or the speed of convergence of finite precision Krylov methods, but helps understanding the principles underlying the behaviour of finite precision Krylov methods.
KeywordsMachine Precision Krylov Subspace Floating Point Step Number Lanczos Method
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