The Experts below are selected from a list of 7182 Experts worldwide ranked by ideXlab platform
Yunkai Zhou - One of the best experts on this subject based on the ideXlab platform.
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software for Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Ron Shepard, Michael Minkoff, Yunkai ZhouAbstract:Abstract This paper describes software for Computing Eigenvalue bounds to the standard and generalized hermitian Eigenvalue problem as described in [Y. Zhou, R. Shepard, M. Minkoff, Computing Eigenvalue bounds for iterative subspace matrix methods , Comput. Phys. Comm. 167 (2005) 90–102]. The software discussed in this manuscript applies to any subspace method , including Lanczos, Davidson , SPAM, Generalized Davidson Inverse Iteration , Jacobi–Davidson, and the Generalized Jacobi–Davidson methods, and it is applicable to either outer or inner Eigenvalues. This software can be applied during the subspace iterations in order to truncate the iterative process and to avoid unnecessary effort when converging specific Eigenvalues to a required target accuracy, and it can be applied to the final set of Ritz values to assess the accuracy of the converged results. Program summary Title of program: SUBROUTINE BOUNDS_OPT Catalogue identifier: ADVE Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVE Computers: any computer that supports a Fortran 90 compiler Operating systems: any computer that supports a Fortran 90 compiler Programming language: Standard Fortran 90 High speed storage required: 5 m + 5 working-precision and 2 m + 7 integer for m Ritz values No. of bits in a word: The floating point working precision is parameterized with the symbolic constant WP No. of lines in distributed program, including test data, etc.: 2452 No. of bytes in distributed program, including test data, etc.: 281 543 Distribution format: tar.gz Nature of physical problem: The computational solution of Eigenvalue problems using iterative subspace methods has widespread applications in the physical sciences and engineering as well as other areas of mathematical modeling (economics, social sciences, etc.). The accuracy of the solution of such problems and the utility of those errors is a fundamental problem that is of importance in order to provide the modeler with information of the reliability of the computational results. Such applications include using these bounds to terminate the iterative procedure at specified accuracy limits. Method of solution: The Ritz values and their residual norms are computed and used as input for the procedure. While knowledge of the exact Eigenvalues is not required, we require that the Ritz values are isolated from the exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum. Using a multipass refinement approach, upper and lower bounds are computed for each Ritz value. Typical running time: While typical applications would deal with m 20 , for m = 100 000 , the running time is 0.12 s on an Apple PowerBook.
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Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Yunkai Zhou, Ron Shepard, Michael MinkoffAbstract:A procedure is presented for the computation of bounds to Eigenvalues of the generalized hermitian Eigenvalue problem and to the standard hermitian Eigenvalue problem. This procedure is applicable to iterative subspace Eigenvalue methods and to both outer and inner Eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the procedure. Knowledge of the exact Eigenvalues is not needed by the procedure, but it must be known that the computed Ritz values are isolated from exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum range. A multipass refinement procedure is described to compute the bounds for each Ritz value. This procedure requires O(m) effort where m is the subspace dimension for each pass.
Zhongsheng Liu - One of the best experts on this subject based on the ideXlab platform.
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a method for Computing Eigenvalue bounds in structural vibration systems with interval parameters
Computers & Structures, 1994Co-Authors: Suhuan Chen, Zhiping Qiu, Zhongsheng LiuAbstract:Abstract A method is presented for Computing the upper and lower bounds of the Eigenvalues for structural vibration systems with interval parameters. As an indication of the effectiveness of this method, a numerical example is presented. The numerical example shows that the method proves to be both effective and valid.
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perturbation method for Computing Eigenvalue bounds in structural vibration systems with interval parameters
Communications in Numerical Methods in Engineering, 1994Co-Authors: Suhuan Chen, Ziping Qiu, Zhongsheng LiuAbstract:In this study a perturbation method for Computing the upper and lower bounds of Eigenvalues of structural vibration systems with interval parameters is presented. The eigenproblem of the uncertain (interval) structure is expressed by equations consisting of the uncertainties. If the uncertainity is small in parameters, the eigensolutions of uncertain structures can be obtained efficiently by the perturbation method presented. A numerical example is given to demonstrate the validity of the method.
Suhuan Chen - One of the best experts on this subject based on the ideXlab platform.
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the rayleigh quotient iteration method for Computing Eigenvalue bounds of structures with bounded uncertain parameters
Computers & Structures, 1995Co-Authors: Zhiping Qiu, Suhuan Chen, Hongbo JiaAbstract:Abstract When the parameters of structures are uncertain, structural natural frequencies become uncertain. In this paper, we deal with the vibration problem of structural parameters with interval uncertainty; the Eigenvalue problem of the structures with interval uncertain parameters is transformed into two different Eigenvalue problems to be solved. The Rayleigh quotient iteration method is applied to the vibration problem of the structures with interval parameters; the numerical results show that the proposed method is sufficiently accurate and requires little computational effort.
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a method for Computing Eigenvalue bounds in structural vibration systems with interval parameters
Computers & Structures, 1994Co-Authors: Suhuan Chen, Zhiping Qiu, Zhongsheng LiuAbstract:Abstract A method is presented for Computing the upper and lower bounds of the Eigenvalues for structural vibration systems with interval parameters. As an indication of the effectiveness of this method, a numerical example is presented. The numerical example shows that the method proves to be both effective and valid.
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perturbation method for Computing Eigenvalue bounds in structural vibration systems with interval parameters
Communications in Numerical Methods in Engineering, 1994Co-Authors: Suhuan Chen, Ziping Qiu, Zhongsheng LiuAbstract:In this study a perturbation method for Computing the upper and lower bounds of Eigenvalues of structural vibration systems with interval parameters is presented. The eigenproblem of the uncertain (interval) structure is expressed by equations consisting of the uncertainties. If the uncertainity is small in parameters, the eigensolutions of uncertain structures can be obtained efficiently by the perturbation method presented. A numerical example is given to demonstrate the validity of the method.
Michael Minkoff - One of the best experts on this subject based on the ideXlab platform.
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software for Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Ron Shepard, Michael Minkoff, Yunkai ZhouAbstract:Abstract This paper describes software for Computing Eigenvalue bounds to the standard and generalized hermitian Eigenvalue problem as described in [Y. Zhou, R. Shepard, M. Minkoff, Computing Eigenvalue bounds for iterative subspace matrix methods , Comput. Phys. Comm. 167 (2005) 90–102]. The software discussed in this manuscript applies to any subspace method , including Lanczos, Davidson , SPAM, Generalized Davidson Inverse Iteration , Jacobi–Davidson, and the Generalized Jacobi–Davidson methods, and it is applicable to either outer or inner Eigenvalues. This software can be applied during the subspace iterations in order to truncate the iterative process and to avoid unnecessary effort when converging specific Eigenvalues to a required target accuracy, and it can be applied to the final set of Ritz values to assess the accuracy of the converged results. Program summary Title of program: SUBROUTINE BOUNDS_OPT Catalogue identifier: ADVE Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVE Computers: any computer that supports a Fortran 90 compiler Operating systems: any computer that supports a Fortran 90 compiler Programming language: Standard Fortran 90 High speed storage required: 5 m + 5 working-precision and 2 m + 7 integer for m Ritz values No. of bits in a word: The floating point working precision is parameterized with the symbolic constant WP No. of lines in distributed program, including test data, etc.: 2452 No. of bytes in distributed program, including test data, etc.: 281 543 Distribution format: tar.gz Nature of physical problem: The computational solution of Eigenvalue problems using iterative subspace methods has widespread applications in the physical sciences and engineering as well as other areas of mathematical modeling (economics, social sciences, etc.). The accuracy of the solution of such problems and the utility of those errors is a fundamental problem that is of importance in order to provide the modeler with information of the reliability of the computational results. Such applications include using these bounds to terminate the iterative procedure at specified accuracy limits. Method of solution: The Ritz values and their residual norms are computed and used as input for the procedure. While knowledge of the exact Eigenvalues is not required, we require that the Ritz values are isolated from the exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum. Using a multipass refinement approach, upper and lower bounds are computed for each Ritz value. Typical running time: While typical applications would deal with m 20 , for m = 100 000 , the running time is 0.12 s on an Apple PowerBook.
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Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Yunkai Zhou, Ron Shepard, Michael MinkoffAbstract:A procedure is presented for the computation of bounds to Eigenvalues of the generalized hermitian Eigenvalue problem and to the standard hermitian Eigenvalue problem. This procedure is applicable to iterative subspace Eigenvalue methods and to both outer and inner Eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the procedure. Knowledge of the exact Eigenvalues is not needed by the procedure, but it must be known that the computed Ritz values are isolated from exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum range. A multipass refinement procedure is described to compute the bounds for each Ritz value. This procedure requires O(m) effort where m is the subspace dimension for each pass.
Ron Shepard - One of the best experts on this subject based on the ideXlab platform.
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software for Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Ron Shepard, Michael Minkoff, Yunkai ZhouAbstract:Abstract This paper describes software for Computing Eigenvalue bounds to the standard and generalized hermitian Eigenvalue problem as described in [Y. Zhou, R. Shepard, M. Minkoff, Computing Eigenvalue bounds for iterative subspace matrix methods , Comput. Phys. Comm. 167 (2005) 90–102]. The software discussed in this manuscript applies to any subspace method , including Lanczos, Davidson , SPAM, Generalized Davidson Inverse Iteration , Jacobi–Davidson, and the Generalized Jacobi–Davidson methods, and it is applicable to either outer or inner Eigenvalues. This software can be applied during the subspace iterations in order to truncate the iterative process and to avoid unnecessary effort when converging specific Eigenvalues to a required target accuracy, and it can be applied to the final set of Ritz values to assess the accuracy of the converged results. Program summary Title of program: SUBROUTINE BOUNDS_OPT Catalogue identifier: ADVE Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVE Computers: any computer that supports a Fortran 90 compiler Operating systems: any computer that supports a Fortran 90 compiler Programming language: Standard Fortran 90 High speed storage required: 5 m + 5 working-precision and 2 m + 7 integer for m Ritz values No. of bits in a word: The floating point working precision is parameterized with the symbolic constant WP No. of lines in distributed program, including test data, etc.: 2452 No. of bytes in distributed program, including test data, etc.: 281 543 Distribution format: tar.gz Nature of physical problem: The computational solution of Eigenvalue problems using iterative subspace methods has widespread applications in the physical sciences and engineering as well as other areas of mathematical modeling (economics, social sciences, etc.). The accuracy of the solution of such problems and the utility of those errors is a fundamental problem that is of importance in order to provide the modeler with information of the reliability of the computational results. Such applications include using these bounds to terminate the iterative procedure at specified accuracy limits. Method of solution: The Ritz values and their residual norms are computed and used as input for the procedure. While knowledge of the exact Eigenvalues is not required, we require that the Ritz values are isolated from the exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum. Using a multipass refinement approach, upper and lower bounds are computed for each Ritz value. Typical running time: While typical applications would deal with m 20 , for m = 100 000 , the running time is 0.12 s on an Apple PowerBook.
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Computing Eigenvalue bounds for iterative subspace matrix methods
Computer Physics Communications, 2005Co-Authors: Yunkai Zhou, Ron Shepard, Michael MinkoffAbstract:A procedure is presented for the computation of bounds to Eigenvalues of the generalized hermitian Eigenvalue problem and to the standard hermitian Eigenvalue problem. This procedure is applicable to iterative subspace Eigenvalue methods and to both outer and inner Eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the procedure. Knowledge of the exact Eigenvalues is not needed by the procedure, but it must be known that the computed Ritz values are isolated from exact Eigenvalues outside of the Ritz spectrum and that there are no skipped Eigenvalues within the Ritz spectrum range. A multipass refinement procedure is described to compute the bounds for each Ritz value. This procedure requires O(m) effort where m is the subspace dimension for each pass.