TRLAN is a program designed to find a small number of extreme eigenvalues and their corresponding eigenvectors of a real symmetric matrix. Denote the matrix as A, the eigenvalue as {lambda}, and the corresponding eigenvector as x, they are defined by the following equation, Ax = {lambda}x. There are a number of different implementations of the Lanczos algorithm available. Why another one? Our main motivation is to develop a specialized version that only target the case where one wants both eigenvalues and eigenvectors of a large real symmetric eigenvalue problems that can not use the shift-and-invert scheme. In this case …
continued below
Publisher Info:
Lawrence Berkeley National Lab., CA (United States)
Place of Publication:
California
Provided By
UNT Libraries Government Documents Department
Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.
Descriptive information to help identify this report.
Follow the links below to find similar items on the Digital Library.
Description
TRLAN is a program designed to find a small number of extreme eigenvalues and their corresponding eigenvectors of a real symmetric matrix. Denote the matrix as A, the eigenvalue as {lambda}, and the corresponding eigenvector as x, they are defined by the following equation, Ax = {lambda}x. There are a number of different implementations of the Lanczos algorithm available. Why another one? Our main motivation is to develop a specialized version that only target the case where one wants both eigenvalues and eigenvectors of a large real symmetric eigenvalue problems that can not use the shift-and-invert scheme. In this case the standard non-restarted Lanczos algorithm requires one to store a large number of Lanczos vectors which can cause storage problem and make each iteration of the method very expensive. The underlying algorithm of TRLAN is a dynamic thick-restart Lanczos algorithm. Like all restarted methods, the user can choose how many vectors can be generated at once. Typically, th e user chooses a moderate size so that all Lanczos vectors can be stored in core. This allows the restarted methods to execute efficiently. This implementation of the thick-restart Lanczos method also uses the latest restarting technique, it is very effective in reducing the time required to compute a desired solutions compared to similar restarted Lanczos schemes, e.g., ARPACK.
This report is part of the following collection of related materials.
Office of Scientific & Technical Information Technical Reports
Reports, articles and other documents harvested from the Office of Scientific and Technical Information.
Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.
