Showing papers on "Tridiagonal matrix algorithm published in 1978"
TL;DR: This work was supported m part by the National Science Foundation under Grant NSF DCR 7307998, in partBy the Energy Research and Development Administration under Grant US ERDA E(ll-1) 2383, and in part by Yale University under a grant subcontracted from the United States Air Force Office of Scmntific Research.
Abstract: Received 17 June 1977 and 8 November 1977. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for chrect commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machmery. To copy otherwise, or to repubhsh, requires a fee and/or specific permission. This work was supported m part by the National Science Foundation under Grant NSF DCR 7307998, in part by the Energy Research and Development Administration under Grant US ERDA E(ll-1) 2383, and in part by Yale University under a grant subcontracted from the United States Air Force Office of Scmntific Research Author's address. Department of Computer Sciences, Painter 328, The Umverslty of Texas at Austin, Austin, TX 78712. @) 1978 ACM 0098-3500/78/1200-0391 $00.75
39 citations
TL;DR: In this article, it was shown that the restriction that all pivots are to be chosen along the main diagonal can be removed without loss of generality, and the restriction on the number of pivots that can be chosen in a symmetric matrices can also be removed.
8 citations
TL;DR: Algorithms BANDSQ and BDSQMX are presented which require N2b in-core words but minimize the number of retrieving and restoring the direct-access records during the Gaussian elimination of the structural stiffness matrix.
Abstract: Based on direct-access programming, algorithms have been developed for the generation, and solution by Gaussian elimination of the structural stiffness matrix equation resulted from application of the finite element method in engineering analyses. A large disk storage is used to store the rows of the stiffness matrix as directly accessible records. The developed algorithm BAND2R requires only 2Nb in-core words in implementing the Gaussian elimination where Nb is the semi-band width of the stiffness matrix. Algorithms BANDSQ and BDSQMX are presented which require N2b in-core words but minimize the number of retrieving and restoring the direct-access records during the Gaussian elimination. BANDSQ has the direct-access feature in both the elimination and backward-substitution steps whereas BDSQMX has the direct-access feature only in the backward-substitution step of the Gaussian elimination. Illustrative applications of the developed algorithms are given and the computer core and time requirements for BAND2R, BANDSQ and BDSQMX are compared to those for the conventional Gaussian elimination of using sequential, in-core storages. Methods for reducing the semi-band width Nb of the structural stiffness matrix are also discussed.
5 citations
TL;DR: In this paper, the potential flow on a blade-to-blade surface of a turbomachine was analyzed using the Thomas algorithm and the numerical properties of resulting non-linear simultaneous equations were studied with respect to grid aspect ratios and convergence.
Abstract: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
3 citations
TL;DR: In this paper, a two-phase method was proposed to solve a set of nonequilibrium material balance equations for liquid extractors and vapor absorbers. But it is applicable only to conventional distillation columns.
2 citations
TL;DR: The conclusion is that partial pivoting codes perform well and that they should be considered for sparse problems whenever pivoting for numerical stability is reqmred.
Abstract: We compare several algorithms for sparse Gaussian elimination with column interchanges. The algorithms are all derived from the same basic elinunatmn scheme, and they (hffer mainly m lmplementatmn details. We examine their theoretmal behavior and compare thetr performances on a number of test problems with that of a high quality complete threshold pwotmg code. Our conclusion is that partial pivoting codes perform qmte well and that they should be considered for sparse problems whenever pivoting for numerical stability is reqmred.
TL;DR: The set of Fortran subroutines discussed an implementation of the algorithm for finding the eigenvectors, x, and eigenvalues, lambda, such that Ax = lambdax, which is believed to be the most efficient procedure available for computing all the Eigenvalues or the complete eigensystem for the indicated classes of matrices.
Abstract: The set of Fortran subroutines discussed an implementation of the algorithm for finding the eigenvectors, x, and eigenvalues, lambda, such that Ax = lambdax, where A is a real skew-symmetric matrix or a real tridiagonal symmetric matrix with a constant diagonal. The algorithm uses only orthogonal similarity transformations and is believed to be the most efficient procedure available for computing all the eigenvalues or the complete eigensystem for the indicated classes of matrices. The three subroutines of the algorithm and their functions are described as follows: TRIZD--a subroutine that transforms an arbitrary real skew-symmetric matrix to skew-symmetric tridiagonal form by using orthogonal similarity transformations; IMZD--a subroutine that computes the eigenvalues and, optionally, the eigenvectors of a symmetric tridiagonal matrix with zeros on the diagonal or of a skew-symmetric tridiagonal matrix; TBAKZD--a subroutine that computes the eigenvectors of an arbitrary real skew-symmetric matrix by back-transforming the eigenvectors of the corresponding skew-symmetric tridiagonal matrix determined by TRIZD. The subroutines TRIZD, IMZD, and TBAKZD have been tested extensively on an IBM 360/91 computer using double precision arithmetic. Complete subroutine listings are available. (RWR)