The Experts below are selected from a list of 144 Experts worldwide ranked by ideXlab platform

Axel Ruhe - One of the best experts on this subject based on the ideXlab platform.

  • rational krylov a practical algorithm for large sparse nonsymmetric matrix pencils
    SIAM Journal on Scientific Computing, 1998
    Co-Authors: Axel Ruhe
    Abstract:

    The rational Krylov algorithm computes eigenvalues and Eigenvectors of a regular not necessarily symmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, where several factorizations with different shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil approximates the solution of the original pencil. Different types of Ritz values and harmonic Ritz values are described and compared. Periodical purging of uninteresting directions reduces the size of the basis and makes it possible to compute many Linearly Independent Eigenvectors and principal vectors of pencils with multiple eigenvalues. Relations to iterative methods are established. Results are reported for two large test examples. One is a symmetric pencil coming from a finite element approximation of a membrane; the other is a nonsymmetric matrix modeling an idealized aircraft stability problem.

  • Rational Krylov, A Practical Algorithm for Large
    1995
    Co-Authors: Axel Ruhe
    Abstract:

    The Rational Krylov algorithm computes eigenvalues and Eigenvectors of a regular not necessarily asymmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, where several factorization with different shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil approximates the solution of the original pencil. Different types of Ritz values and harmonic Ritz values are described and compared. Periodical purging of uninteresting directions reduces the size of the basis, and makes it possible to get many Linearly Independent Eigenvectors and principal vectors to pencil with multiple eigenvalues. Relations to iterative methods are established. Results are reported for two large test examples. One is a symmetric pencil coming from a finite element approximation of a membrane, the other a nonsymmetric matrix modeling an idealized aircraft stability problem.

  • Rational Krylov, A Practical Algorithm For Large Sparse Nonsymmetric Matrix Pencils
    1995
    Co-Authors: Axel Ruhe
    Abstract:

    . The Rational Krylov algorithm computes eigenvalues and Eigenvectors of a regular not necessarily symmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, where several factorizations with different shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil approximates the solution of the original pencil. Different types of Ritz values and harmonic Ritz values are described and compared. Periodical purging of uninteresting directions reduces the size of the basis, and makes it possible to get many Linearly Independent Eigenvectors and principal vectors to pencils with multiple eigenvalues. Relations to iterative methods are established. Results are reported for two large test examples. One is a symmetric pencil coming from a finite element approximation of a membrane, the other a nonsymmetric matrix modeling an idealized aircraft stability problem. Key words. matrix, eig..

Patrick Patrick Anderson - One of the best experts on this subject based on the ideXlab platform.

  • An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method
    Physics of Fluids, 2012
    Co-Authors: O Oleksandr Gorodetskyi, Mfm Michel Speetjens, Patrick Patrick Anderson
    Abstract:

    The mapping method is an efficient tool to investigate distributive mixing induced by periodic flows. Computed only once, the mapping matrix can be applied a number of times to determine the distribution of concentration inside the flow domain. Spectral analysis of the mapping matrix reveals detailed properties of the distributive mixing as all relevant information is stored in its eigenmodes. Any vector that describes a distribution of concentration can be expanded in the complete system of Linearly Independent Eigenvectors of the mapping matrix. The rapid decay of the contribution of each mode in the eigenmode decomposition allows for a truncation of the eigenmode expansion from the whole spectrum to only the dominant eigenmodes (characterized by a decay rate significantly lower than the duration of the mixing process). This truncated decomposition adequately represents the distribution of concentration inside the flow domain already after a low number of periods, because contributions of all non-domina...

Nobuyuki Aiba - One of the best experts on this subject based on the ideXlab platform.

  • Eigenstructure-preserving scheme for a hyperbolic system
    arXiv: Computational Physics, 2019
    Co-Authors: Takashi Shiroto, Akinobu Matsuyama, Nobuyuki Aiba
    Abstract:

    A hyperbolic system must have a set of Linearly Independent Eigenvectors and corresponding real eigenvalues. In numerical simulations, however, the eigenvalues can be complex because truncation errors pollute a characteristic polynomial of the hyperbolic system. Here we propose an eigenstructure-preserving scheme which always generates the real eigenvalues, even in discrete level. Although the eigenstructure is discussed in a non-conservative formulation, the proposed scheme is locally conservative owing to the skew-symmetric operators.

O Oleksandr Gorodetskyi - One of the best experts on this subject based on the ideXlab platform.

  • An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method
    Physics of Fluids, 2012
    Co-Authors: O Oleksandr Gorodetskyi, Mfm Michel Speetjens, Patrick Patrick Anderson
    Abstract:

    The mapping method is an efficient tool to investigate distributive mixing induced by periodic flows. Computed only once, the mapping matrix can be applied a number of times to determine the distribution of concentration inside the flow domain. Spectral analysis of the mapping matrix reveals detailed properties of the distributive mixing as all relevant information is stored in its eigenmodes. Any vector that describes a distribution of concentration can be expanded in the complete system of Linearly Independent Eigenvectors of the mapping matrix. The rapid decay of the contribution of each mode in the eigenmode decomposition allows for a truncation of the eigenmode expansion from the whole spectrum to only the dominant eigenmodes (characterized by a decay rate significantly lower than the duration of the mixing process). This truncated decomposition adequately represents the distribution of concentration inside the flow domain already after a low number of periods, because contributions of all non-domina...

Zekeriya Uykan - One of the best experts on this subject based on the ideXlab platform.

  • On the "SIR"s ("Signal"-to-"Interference"-Ratio) in Discrete-Time Autonomous Linear Networks
    2009 Computation World: Future Computing Service Computation Cognitive Adaptive Content Patterns, 2009
    Co-Authors: Zekeriya Uykan
    Abstract:

    A Hopfield-like neural network, called SALU-SIR,whose system weight matrix is symmetric is presented withits mathematical analysis in [7]. However, what happens if the system matrix is unsymmetric? Is the system still stable in the unsymmetric case? In this paper, we address these importantquestions, whose answer is paramount especially when the system is to be implemented in practice.The underlying linear system of the proposed network is x(k+1) = Ax(k)+b where A is any real square unsymmetric matrix with Linearly Independent Eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector b is constant. Our investigations in this paper show that i) the unsymmetric case is also stable; ii) the unsymmetric case yields state-specific ultimate SIRs as compared to the system-specific ultimate SIR in the symmetric case [7], which allows us to design more complex systems. iii) the ultimate “SIR”s in the investigated unsymmetric matrix A case are equal to aiiλmax−aii , i = 1, 2, . . . , N, where Nis the number of states, aii is the diagonal elements of matrix A, and λmax is the (single or multiple) eigenvalue with maximum norm.Possible applications include binary associative memory systems, image restoration, etc in the area of artificial intelligence and cognition.

  • Discrete-Time Autonomous Linear Networks
    1
    Co-Authors: Zekeriya Uykan
    Abstract:

    In this letter, we improve the results in [5] by relaxing the symmetry assumption and also taking the noise term into account. The author examines two discrete-time autonomous linear systems whose motivation comes from a neural network point of view in [5]. Here, we examine the following discretetime autonomous linear system: x(k+1) = Ax(k)+b where A is any real square matrix with Linearly Independent Eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector b is constant. Using the same “SIR ” (“Signal”-to-“Interference”-Ratio) concept as in [4] and [5], we show that the ultimate “SIR ” is equal to aii, i = 1, 2,...,N, where N is the number of states, aii λmax−aii is the diagonal elements of matrix A, and λmax is the (single or multiple) eigenvalue with maximum norm