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  • Engineering  (3)
  • Galerkin condition  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Generalizations and modifications of the GMRES iterative method (1999)
    Springer
    Numerical algorithms 21 (1999), S. 119-146 
    Details
    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
    URL: http://dx.doi.org/10.1023/A:1019105328973
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  • 2
    Electronic Resource
    Electronic Resource
    A dual adaptive procedure for the automatic determination of iteration parameters for Chebyshev acceleration (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 483-499 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Chebyshev acceleration for a symmetrizable basic iterative method u(n+1) = Gu(n) + k; requires estimates of the extreme eigenvalues m(G) and M(G) of the iteration matrix G. Adaptive procedures are often used in order to obtain good estimates for m(G) and M(G). Some existing adaptive procedures are able to give an estimate of either m(G) or M(G) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m(G) and M(G) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270305
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  • 3
    Electronic Resource
    Electronic Resource
    Vectorized iterative methods for partial differential equations (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 289-296 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020310
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  • 4
    Electronic Resource
    Electronic Resource
    Iterative algorithms and software for solving large sparse linear systems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 435-456 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper is concerned with iterative algorithms for solving systems of linear algebraic equations where the coefficient matrix is large and sparse. Such systems often arise in the numerical solution of partial differential equations by finite difference or finite element methods. The algorithms considered include a basic iterative method, an acceleration procedure for speeding up the convergence of the basic iterative method and an adaptive procedure for determining any necessary iteration parameters. Algorithms are described both for the case where the coefficient matrix is symmetric and positive definite and for the nonsymmetrizable case. The ITPACK Project was established by the Center for Numerical Analysis at The University of Texas in 1974. The object of ITPACK was the study of iterative algorithms, using both theoretical and experimental methods. Several software packages are described which have been developed as part of the ITPACK project for carrying out experimental studies with a variety of algorithms over a wide range of problems. Recent work on the use of advanced computer architectures is briefly discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630040318
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