ISBN-10: 0511082088

ISBN-13: 9780511082085

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According to the article [116] written by Magnus R. Hestenes, he and Eduard Stiefel developed the CG algorithm independently. Stiefel was visiting the Institute for Numerical Analysis (INA) of the University of California, Los Angeles (UCLA), USA, due to a conference in 1951, where he got a copy of an INA report which Hestenes wrote on the CG method. ” Hestenes invited Stiefel to stay for one semester at UCLA and INA where they wrote together their famous paper [117]. 34 3 Block Krylov Methods symmetric and positive definite.

Note that we have to compute all eigenvectors in order to determine the corresponding CS metrics which are needed to choose finally the D eigenvectors with the largest sum of metrics. Thus, the complexity order of the CS method is cubic, i. 1. Due to this reason, we present the CS based reduced-rank MWF only as a bound for the best-possible MWF approximation in an eigensubspace. , e. , [87]). In such scenarios, it has been observed that compared to the PC based approach, the rank of the CS based MWF approximation can even be chosen smaller than the dimension of the signal subspace, i.

To compute the solution of the system LV = Cy ,x of linear equations. For i ∈ {0, 1, . . 24) [L]0,0 [V ]0,: , i = 0, [L]i,i [V ]i,: + [L]i,0:i−1 [V ]0:i−1,: , i ∈ {1, 2, . . , N − 1}, N > 1, if we exploit the lower triangular structure of L, i. , the fact that the elements of the (i + 1)th row with an index higher than i are zero, and where we separated [L]i,i [V ]i,: from the given sum. Note that ‘:’ is the abbreviation for ‘0 : z’ where z is the maximum value of the index under consideration.

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Linear Estimation and Detection in Krylov Subspaces

by George

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