# LREP

AcronymDefinition
LREPLine Repeater
LREPLand Resource Evaluation and Planning (Asian Development Bank)
LREPLegal Research for Estate Planners (online resource; est. 1997; attorney Jason Havens)
LREPLawyer Referral for the Elderly Program (New Mexico Bar Association)
LREPLong Range Exclusion Process
LREPLightweight Replica
LREPLimited-Route Explorer Packet (Cisco)
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References in periodicals archive ?
This is particularly important for LREP because only the first small portion of the eigenvalues, i.e., [[lambda].sub.j] in (1.4) for i = 1,..., k with k << N, are of interest.
To alleviate these and to make it more practical, we incorporate a restarting procedure to our block Lanczos method for LREP. There are several types of restarting schemes for the classic Lanczos method for the symmetric eigenvalue problem, including the implicitly restart method [9, 16], the Krylov-Schur method [17], and the thick-restart method [25, 26]; by considering the special structure of LREP, the thick-restart method of [25, 26] turns out to be efficient and is used in this paper.
In Section 2 we collect some basic results for LREP and M-canonical angles for two subspaces that are used frequently in our later developments.
Block Lanczos process for LREP. The first Lanczos process for LREP presented in [19] is a partial realization of the decomposition in Lemma 2.3.
When [n.sub.b] = 1, Algorithm 3.1 reduces to the single-vector Lanczos process for LREP in [19].
Basically the block Lanczos method for LREP is this block Lanczos process followed by solving the small scale LREP for [H.sub.n] to obtain approximate eigenpairs for H in (1.1).
Algorithm 3.1 A block Lanczos process for LREP. Input: Choose [U.sub.0], [mathematical expression not reproducible] such that rank([V.sub.0]) = [n.sub.b], M[V.sub.0] = [U.sub.0] and an integer n [greater than or equal to] 1.
Here, the cluster is described in terms of the squares of the eigenvalues since the eigenvalues of LREP come in pairs {- [lambda], [lambda]} and they may be purely imaginary numbers.
Recalling (3.1) and (3.2), we know that the quantities computed by the block Lanczos method (Algorithm 3.1) satisfy the following relationship for LREP,
For our case, the LREP, the thick-restart technique [25, 26] appears to be an effective one, and we describe the detailed procedure in this section.
To save the costs of forming larger subspaces in the block Lanczos process and to reduce the costs in the Ritz procedure for solving the resulting LREP for larger n[n.sub.b], the iteration is restarted after the basis vector [V.sub.n+1] has been computed.
We summarize what we have obtained in this section in Algorithm 4.1, the thick-restart block Lanczos Algorithm for LREP. We denote it by BlanLR(n, k) where the indices n and k are the parameters for the thick-restart.
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