The Lanczos Method: Evolution and ApplicationSIAM, 1 de gen. 2003 - 99 pàgines The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications drawn from the author's experience. These chapters provide a unique interaction between the numerical algorithms and their engineering applications. This is a valuable reference for numerical analysts and engineers and can be used as a supplementary or reference text at the graduate level. Readers should be familiar with basic linear algebra and numerical analysis. |
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acceptance advantage algorithm analysis application appropriate approximate assume biorthogonality block boundary breakdown calculated called Chapter complex components computational condition containing continuity convergence corresponding damping direct discussed domain decomposition eigenvalue problem eigenvectors engineering equation error exact arithmetic example executed fact factorization Finally finite precision fluid forced frequency function further geometric given global implementation important industrial inner product interest Introducing issues iteration Lanczos method Lanczos process Lanczos vectors Lanczos’s linear loss of orthogonality machine epsilon maintaining mathematical multiple norm normal Note obtain operation original orthogonal matrix parallel partitions physical polynomial practical presented procedure processor recurrence represents respectively resulting segments shift shown singular solution solve Specifically spectral transformation steps structural substitution symmetric technique tridiagonal matrix University unsymmetric usually various vibration yields zero