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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 72 (1992), S. 415-440 
    ISSN: 1573-2878
    Keywords: Iterative methods ; Krylov subspaces ; conjugate gradient methods ; sparse matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising in applications to differential equations. We focus on an application derived from a seismic inverse problem. The linear system is a small perturbation to a symmetric positive-definite system, the nonsymmetries arising from discretization errors in the solution of certain boundary-value problems. We state and prove a new error bound for a class of generalized conjugate residual methods; we show that, in some cases, the perturbed symmetric problem can be solved with an error bound similar to the one for the conjugate residual method applied to the symmetric problem. We also discuss several applications for special distributions of eigenvalues.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 72 (1992), S. 441-457 
    ISSN: 1573-2878
    Keywords: Iterative methods ; Krylov subspaces ; conjugate gradient methods ; nonsymmetric matrices ; deflated decompositions ; sparse matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the use of Krylov subspace methods for the solution of nearly singular nonsymmetric linear systems. We show that the incomplete orthogonalization methods (IOM) in conjunction with certain deflation techniques of Stewart, Chan, and Saad can be used to solve large nonsymmetric linear systems which are nearly singular.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 277-290 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We compare three global configuration search methods on a scalable model problem to measure relative performance over a range of molecule sizes. Our model problem is a 2-D polymer composed of atoms connected by rigid rods in which all pairs of atoms interact via Lennard-Jones potentials. The global minimum energy can be calculated analytically. The search methods are all hybrids combining a global sampling algorithm with a local refinement technique. The sampling methods are simulated annealing (SA), genetic algorithms (GA), and random search. Each of these uses a conjugate gradient (CG) routine to perform the local refinement. Both GA and SA perform progressively better relative to random search as the molecule size increases. We also test two other local refinement techniques in addition to CG, coupled to random search as the global method. These are simplex followed by CG and simplex followed by block-truncated Newton. For small problems, the addition of the intermediate simplex step improved the performance of the overall hybrid method. © 1992 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 17 (1996), S. 1142-1151 
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We present results from the application of two conformational searching methods: genetic algorithms (GA) and direct search methods for finding low energy conformations of organic molecules. GAs are in a class of biologically motivated optimization methods that evolve a population of individuals in which individuals who are more “fit” have a higher probability of surviving into subsequent generations. The parallel direct search method (PDS) is a type of pattern search method that uses an adaptive grid to search for minima. Both methods found energies equal to or lower than the energy of the relaxed crystal structure in all cases, at a relatively small cost in CPU time. We suggest that either method would be a good candidate to find 3-D conformations in a large scale screening application. © 1996 by John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 15 (1994), S. 627-632 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules, which depends on the accurate determination of their three-dimensional structure, can be formulated as a global optimization problem. In this article, we present results from the application of a new conformation searching method based on direct search methods. We compare these results to some earlier results using genetic algorithms and simulated annealing. © 1994 by John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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