A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration
نویسندگان
چکیده
منابع مشابه
A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration
Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, sharp non-asymptotic convergence estimates are known. These estimates require a properly scaled preconditioner. In t...
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By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving Hermitian-definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotic estimate of the rate of convergence of the PSD-id method. We show t...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2012
ISSN: 0036-1429,1095-7170
DOI: 10.1137/11084488x