The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Jacek Matulewski - One of the best experts on this subject based on the ideXlab platform.
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an object oriented c implementation of davidson method for finding a few selected extreme eigenpairs of a large sparse Real Symmetric Matrix
Computer Physics Communications, 2007Co-Authors: Tomasz Dziubak, Jacek MatulewskiAbstract:Abstract A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, Real, Symmetric Matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrodinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers–Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed). The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M. Program summary Program title: Davidson Catalogue identifier: ADZM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 037 055 No. of bytes in distributed program, including test data, etc.: 20 002 609 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Any RAM: User's parameters dependent Word size: 32 and 64 bits Supplementary material: Test results for the 2D and 3D cases is available Classification: 4, 4.8 Nature of problem: Finding a few extreme eigenpairs of a Real, Symmetric, sparse Matrix. Examples in quantum optics (interaction of matter with a laser field). Solution method: Davidson algorithm Running time: The test example included in the distribution package (1D Matrix) takes approximately 30 minutes to run. 2D Matrix calculations can take hours and 3D, days, to run.
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An object-oriented C++ implementation of Davidson method for finding a few selected extreme eigenpairs of a large, sparse, Real, Symmetric Matrix
Computer Physics Communications, 2007Co-Authors: Tomasz Dziubak, Jacek MatulewskiAbstract:Abstract A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, Real, Symmetric Matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrodinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers–Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed). The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M. Program summary Program title: Davidson Catalogue identifier: ADZM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 037 055 No. of bytes in distributed program, including test data, etc.: 20 002 609 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Any RAM: User's parameters dependent Word size: 32 and 64 bits Supplementary material: Test results for the 2D and 3D cases is available Classification: 4, 4.8 Nature of problem: Finding a few extreme eigenpairs of a Real, Symmetric, sparse Matrix. Examples in quantum optics (interaction of matter with a laser field). Solution method: Davidson algorithm Running time: The test example included in the distribution package (1D Matrix) takes approximately 30 minutes to run. 2D Matrix calculations can take hours and 3D, days, to run.
Liping Cao - One of the best experts on this subject based on the ideXlab platform.
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Letter: A simple functional neural network for computing the largest and smallest eigenvalues and corresponding eigenvectors of a Real Symmetric Matrix
Neurocomputing, 2005Co-Authors: Yiguang Liu, Zhisheng You, Liping CaoAbstract:Efficient computation of the largest eigenvalue and the smallest eigenvalue of a Real Symmetric Matrix is a very important problem in engineering. Using neural networks to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a concise functional neural network (FNN) expressed as a differential equation and designs steps to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are fully gained. Finally, the computing steps are designed in detail. The proposed method can compute the smallest eigenvalue and the largest eigenvalue whether the Matrix is non-definite, positive definite or negative definite. Compared with other methods based on neural networks, this FNN is very simple and concise, so it is very easy to Realize.
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A Concise Functional Neural Network Computing the Largest (Smallest) Eigenvalue and one Corresponding Eigenvector of a Real Symmetric Matrix
2005 International Conference on Neural Networks and Brain, 1Co-Authors: Yiguang Liu, Zhisheng You, Liping CaoAbstract:Quick extraction of eigenpairs of a Real Symmetric Matrix is very important in engineering. Using neural networks to complete this operation is in a parallel manner and can achieve high performance. So, this paper proposes a very concise functional neural network (FNN) to compute the largest (or smallest) eigenvalue and one its eigenvector. When the FNN is converted into a differential equation, the component analytic solution of this equation is obtained. Using the component solution, the convergence properties are fully analyzed. On the basis of this FNN, the method that can compute the largest (or smallest) eigenvalue and one its eigenvector whether the Matrix is non-definite, positive definite or negative definite is designed. Finally, three examples show the validity of the method. Comparing with other neural networks designed for the same aim, the proposed FNN is very simple and concise, so it is very easy to be Realized
Charlotte Froese Fischer - One of the best experts on this subject based on the ideXlab platform.
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A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, Real, Symmetric Matrix
Computer Physics Communications, 1994Co-Authors: Andreas Stathopoulos, Charlotte Froese FischerAbstract:Abstract A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, Real, Symmetric Matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the original algorithm by adopting several extensions. The Matrix-vector multiplication routine that it requires is to be provided by the user. Different Matrix formats and optimizations are thus feasible. Examples of an efficient sparse Matrix representation and a Matrix-vector multiplication are given. Some comparisons with the Lanczos method demonstrate the efficiency of the program.
Wang Hong-xing - One of the best experts on this subject based on the ideXlab platform.
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Numerical Solution of Prolate Spheroidal Wave Functions Based on Nyquist's Sampling
Radio and communications technology, 2010Co-Authors: Wang Hong-xingAbstract:In order to solve the problems that how to discretize integral equation,and with which methods to obtain eigenvalues and eigenvectors of Real Symmetric Matrix during numerical solution process of Prolate Spheroidal Wave Functions(PSWF),a numerical solution of PSWF based on Nyquist' sampling is proposed.The method discretizes integral equation by making use of sampling frequency which is defined by Nyquist' sampling theorem.All the eigenvalues and corresponding eigenvectors of Real Symmetric Matrix are obtained by use of Jacobi's method.The eigenvector is just the approximate numerical solution of PSWF.Theoretical deduction,performance analysis and simulation are conducted for numerical solution of PSWF.Theoretical analysis and simulation results show that the method is simple and applicable,the achieved PSWF are with high precision and the orthogonality between PSWF is good.
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Design Method of Prolate Spheroidal Wave Pulse Signals Based on Nyquist's Sampling
Journal of China Academy of Electronics and Information Technology, 2010Co-Authors: Wang Hong-xingAbstract:In order to solve the problems that how to discretize integral equation,and with which method to achieve eigenvalues and eigenvectors of Real Symmetric Matrix during the design process of prolate spheroidal wave pulse signals,a design method of prolate spheroidal wave pulse signals based on Nyquist' sampling is proposed.According to this method,we discretize the integral equation by making use of sampling frequency which is defined by Nyquist' sampling theorem.We could get all the eigenvalues and corresponding eigenvectors of Real Symmetric Matrix by using Jacobi' method.The eigenvectors are just the approximate numerical solutions of prolate spheroidal wave functions.Prolate spheroidal wave pulse signal can be obtained just by horizontally moving the prolate spheroidal wave function rightward along the time axis.Theoretical analysis and simulation results show that the method is simple and practical applicability.The achieved prolate spheroidal wave pulse signal is with high precision and the orthogonality between pulse signals is good.
Tomasz Dziubak - One of the best experts on this subject based on the ideXlab platform.
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an object oriented c implementation of davidson method for finding a few selected extreme eigenpairs of a large sparse Real Symmetric Matrix
Computer Physics Communications, 2007Co-Authors: Tomasz Dziubak, Jacek MatulewskiAbstract:Abstract A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, Real, Symmetric Matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrodinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers–Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed). The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M. Program summary Program title: Davidson Catalogue identifier: ADZM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 037 055 No. of bytes in distributed program, including test data, etc.: 20 002 609 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Any RAM: User's parameters dependent Word size: 32 and 64 bits Supplementary material: Test results for the 2D and 3D cases is available Classification: 4, 4.8 Nature of problem: Finding a few extreme eigenpairs of a Real, Symmetric, sparse Matrix. Examples in quantum optics (interaction of matter with a laser field). Solution method: Davidson algorithm Running time: The test example included in the distribution package (1D Matrix) takes approximately 30 minutes to run. 2D Matrix calculations can take hours and 3D, days, to run.
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An object-oriented C++ implementation of Davidson method for finding a few selected extreme eigenpairs of a large, sparse, Real, Symmetric Matrix
Computer Physics Communications, 2007Co-Authors: Tomasz Dziubak, Jacek MatulewskiAbstract:Abstract A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, Real, Symmetric Matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrodinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers–Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed). The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M. Program summary Program title: Davidson Catalogue identifier: ADZM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 037 055 No. of bytes in distributed program, including test data, etc.: 20 002 609 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Any RAM: User's parameters dependent Word size: 32 and 64 bits Supplementary material: Test results for the 2D and 3D cases is available Classification: 4, 4.8 Nature of problem: Finding a few extreme eigenpairs of a Real, Symmetric, sparse Matrix. Examples in quantum optics (interaction of matter with a laser field). Solution method: Davidson algorithm Running time: The test example included in the distribution package (1D Matrix) takes approximately 30 minutes to run. 2D Matrix calculations can take hours and 3D, days, to run.
