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  • Engineering  (4)
  • 65N20  (1)
  • Lanczos-type methods  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerical algorithms 21 (1999), S. 119-146 
    ISSN: 1572-9265
    Keywords: iterative methods ; Generalized Minimum Residual (GMRES) method ; minimization condition ; Galerkin condition ; Lanczos-type methods ; 65F10 ; 65H10 ; 65N20 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For solving nonsymmetric linear systems, the well-known GMRES method is considered to be a stable method; however, the work per iteration increases as the number of iterations increases. We consider two new iterative methods GGMRES and MGMRES, which are a generalization and a modification of the GMRES method, respectively. Instead of using a minimization condition as in the derivation of GGMRES, we use a Galerkin condition to derive the MGMRES method. We also introduce another new iterative method, LAN/MGMRES, which is designed to combine the reliability of GMRES with the reduced work of a Lanczos-type method. A computer program has been written based on the use of the LAN/MGMRES algorithm for solving nonsymmetric linear systems arising from certain elliptic problems. Numerical tests are presented comparing this algorithm with some other commonly used iterative algorithms. These preliminary tests of the LAN/MGMRES algorithm show that it is comparable in terms of both the approximate number of iterations and the overall convergence behavior.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 589-608 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: NSPCG is the most recent research-oriented software package developed as part of the ITPACK Project at the Center for Numerical Analysis of The University of Texas at Austin. It is designed to solve large sparse systems of linear equations by a variety of different non-symmetric preconditioned conjugate gradient methods. Several different sparse data storage schemes are available for storing the coefficient matrix of the linear system. Matrices with a wide range of structures from highly structured to completely unstructured can be accommodated. To limit memory requirements, the accelerators in the package can be called directly with the matrix stored in a user-defined sparse data storage format (for example, from a particular application) by supplying some user-written routines for certain matrix-vector operations.The main entry point into the package is through a single subroutine call. The various methods are accessed by using a particular naming convention for the first two parameters that in turn selects a preconditioner, an accelerator and a data storage scheme. Some of the basic preconditioners that are available are Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner. One of the main purposes for the development of the package was to provide a common modular structure for research on iterative methods. The entire package is written in Fortran 77 with vectorization in mind for applications on supercomputers.
    Additional Material: 2 Tab.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 289-296 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Tab.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 349-359 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for computing in parallel the general LU factorization of a matrix is presented. As special cases, one obtains the Doolittle, Crout and Cholesky methods. The algorithm was implemented and tested on a Cray X-MP/48.
    Additional Material: 1 Tab.
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  • 5
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Results are presented of the performance of two different versions of the ITPACK software package on large sparse linear systems arising in the solution of sample oil reservoir simulation problems using three different large vector computers (Cyber 205, Cray X-MP48 and Amdahl VP1200). The main focus of this paper is on the necessary changes in the package that were made for efficiency when going from a memory-to-memory computer to a register-to-register computer. We feel that these are typical changes that must be considered when moving software of this type between vector computers. The execution times presented should not be considered to be representative of the overall performance of these computers.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
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