On the Subspace Projected Approximate Matrix method
نویسندگان
چکیده
منابع مشابه
On the Subspace Projected Approximate Matrix Method
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix A. It falls in the category of inner-outer iteration methods and aims to reduce the costs of matrix-vector products with A within its inner iteration. This is done by choosing an approximation A0 of A...
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A modification of the iterative matrix diagonalization method of Davidson is presented that is applicable to the symmetric eigenvalue problem. This method is based on subspace projections of a sequence of one or more approximate matrices. The purpose of these approximate matrices is to improve the efficiency of the solution of the desired eigenpairs by reducing the number of matrix-vector produ...
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Given two n×n matrices A and A0 and a sequence of subspaces {0}=V0 ⊂ · · · ⊂ Vn = R n with dim(Vk) = k, the k-th subspace-projected approximated matrix Ak is defined as Ak = A + Πk(A0 − A)Πk , where Πk is the orthogonal projection on V ⊥ k . Consequently, Ak v = Av and v Ak = v ∗A for all v ∈ Vk. Thus (Ak) n k≥0 is a sequence of matrices that gradually changes from A0 into An = A. In principle,...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 2015
ISSN: 0862-7940,1572-9109
DOI: 10.1007/s10492-015-0104-8