Efficient Numerical Methods For Non Local Operators

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Efficient Numerical Methods For Non Local Operators

Efficient Numerical Methods For Non Local Operators written by Steffen Börm and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense $n\times n$ matrix in standard representation requires $n^2$ units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only $O(n k \log n)$ units of storage, where $k$ is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions, and to solve matrix equations used in control theory. $\mathcal{H}^2$-matrices offer a refinement of hierarchical matrices: Using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This book gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of $\mathcal{H}^2$-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are required only in isolated sections, e.g., for certain classes of model problems.

Hierarchical Matrices Algorithms And Analysis

Hierarchical Matrices Algorithms And Analysis written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-21 with Mathematics categories.

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Proceedings Of The Asme Noise Control And Acoustics Division

Proceedings Of The Asme Noise Control And Acoustics Division written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Acoustic emission categories.

Mathematical Reviews

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

The Journal Of Computational Finance

The Journal Of Computational Finance written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Finance categories.

Recent Advances In Wavelet Analysis

Recent Advances In Wavelet Analysis written by Larry L. Schumaker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book covers recent advances in wavelet analysis and applications in areas including wavelets on bounded intervals, wavelet decomposition of special interest to statisticians, wavelets approach to differential and integral equations, analysis of subdivision operators, and wavelets related to problems in engineering and physics.

Wavelet Applications In Signal And Image Processing

Wavelet Applications In Signal And Image Processing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Image processing categories.

Parallel Computing Technologies

Parallel Computing Technologies written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Parallel processing (Electronic computers) categories.

Dissertation Abstracts International

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Dissertations, Academic categories.

Siam Journal On Numerical Analysis

Siam Journal On Numerical Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02 with Electronic journals categories.