Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Invariant manifolds ; Error estimates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many processes in the sciences and in engineering are modelled by dynamical systems and - in discretized version - by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Preconditioning ; Diagonal compensation ; Eigenvalue bounds ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Korovkin theorem ; Heat conduction equation ; Lax theorem ; Difference scheme ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 5
    ISSN: 1070-5325
    Keywords: mixed finite elements ; hierarchical decomposition ; hybrid V-cycle preconditioner ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we investigate some cost-effective hybrid V-cycle multilevel algorithms for the discrete systems that arise when a mixed finite element approach is used to solve certain second-order elliptic boundary value problems. By introducing a small penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system involving the unknown flux alone. We study the numerical behaviour of some hybrid V-cycle multilevel algorithms with optimal computational complexity based on the hierarchical spatial decomposition approach proposed by Cai, Goldstein and Pasciaks for the reduced system. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: rank deficiency ; bordered matrices ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Rank-deficient matrices arise naturally in many applications. Detecting rank changes and computing parameter values for which a matrix has a prescribed (low) rank deficiency is a fundamental task in computing least squares and minimum norm solutions to systems of linear equations.We describe an approach that originates from numerical continuation and bifurcation theory but has a wider applicability. It uses only linear solves with a bordered extension of the rank-deficient matrix and the transpose of that extension. We discuss the basic methods and their application in fundamental problems such as minimization and in more advanced problems in non-linear analysis. We present extensive numerical evidence in instructive test cases as well as in chemical model (one-dimensional PDE) and a biological model (using the software package CONTENT for dynamical systems). © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: predictor polynomials ; eigenvalues ; companion matrices ; time series ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Predictor polynomials are often used in linear prediction methods mainly for extracting properties of physical systems which are described by time series. The aforementioned properties are associated with a few zeros of large polynomials and for this reason the zero locations of those polynomials must be analyzed. We present a linear algebra approach for determining the zero locations of predictor polynomials, which enables us to generalize some early results obtained by Kumaresan in the signal analysis field. We also present an analysis of zero locations for time series having multiple zeros. © 1997 by John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: complex symmetric matrices ; singular value decomposition ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an algorithm for the approximation of the dominant singular values and corresponding right and left singular vectors of a complex symmetric matrix. The method is based on two short-term recurrences first proposed by Saunders, Simon and Yip [24] for a non-Hermitian linear system solver. With symmetric matrices, the recurrence can be modified so as to generate a tridiagonal symmetric matrix from which the original triplets can be approximated. The recurrence formally resembles the Lanczos method, in spite of substantial differences which make usual convergence results inapplicable. Implementation aspects are discussed, such as re-orthogonalization and the use of alternative representation matrices. The method is very efficient over existing approaches which do not exploit the symmetry of the problem. Numerical experiments on application problems validate the analysis, while showing satisfactory results, especially on dense matrices. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 9
    ISSN: 1070-5325
    Keywords: regular generalized eigenproblem ; condition number ; backward error ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = λBx, when λ is a semi-simple and finite eigenvalue, which departs from the classical analysis with the chordal norm [9]. A backward error and a condition number are derived for a choice of flexible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error associated with an eigenvalue only is also discussed. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: eigenvalues ; Arnoldi ; Krylov subspaces ; preconditioning ; Davidson's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh-Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh-Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...