Approximation By Bounded Analytic Functions Problem Beta
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Approximation By Bounded Analytic Functions Problem Beta
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Author : Joseph Leonard Walsh
language : en
Publisher:
Release Date : 1961
Approximation By Bounded Analytic Functions Problem Beta written by Joseph Leonard Walsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Functions categories.
The problem is the study of approximation to a function f(z) analytic but not bounded in a region D on a closed set E in D. Asymptotic relations concerning degree of approximation are derived. (Author).
Interpolation And Approximation By Rational Functions In The Complex Domain
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Author : Joseph Leonard Walsh
language : en
Publisher:
Release Date : 1965
Interpolation And Approximation By Rational Functions In The Complex Domain written by Joseph Leonard Walsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Functions categories.
Selected Papers
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Author : Joseph L. Walsh
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-11
Selected Papers written by Joseph L. Walsh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-11 with Mathematics categories.
This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".
Afosr
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Author : United States. Air Force. Office of Scientific Research
language : en
Publisher:
Release Date : 1957
Afosr written by United States. Air Force. Office of Scientific Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Research categories.
Technical Abstract Bulletin
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Author :
language : en
Publisher:
Release Date :
Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
U S Government Research Reports
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Author :
language : en
Publisher:
Release Date : 1962
U S Government Research Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Science categories.
Transactions Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1961
Transactions Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Electronic journals categories.
Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.
Bulletin Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1975
Bulletin Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Proceedings Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1959
Proceedings Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Electronic journals categories.
Contains the material formerly published in even-numbered issues of the Bulletin of the American Mathematical Society.
Eigenvalue Analysis And Convergence Acceleration Techniques For Summation By Parts Approximations
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Author : Andrea Alessandro Ruggiu
language : en
Publisher: Linköping University Electronic Press
Release Date : 2019-09-05
Eigenvalue Analysis And Convergence Acceleration Techniques For Summation By Parts Approximations written by Andrea Alessandro Ruggiu and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with categories.
Many physical phenomena can be described mathematically by means of partial differential equations. These mathematical formulations are said to be well-posed if a unique solution, bounded by the given data, exists. The boundedness of the solution can be established through the so-called energy-method, which leads to an estimate of the solution by means of integration-by-parts. Numerical approximations mimicking integration-by-parts discretely are said to fulfill the Summation-By-Parts (SBP) property. These formulations naturally yield bounded approximate solutions if the boundary conditions are weakly imposed through Simultaneous-Approximation-Terms (SAT). Discrete problems with bounded solutions are said to be energy-stable. Energy-stable and high-order accurate SBP-SAT discretizations for well-posed linear problems were first introduced for centered finite-difference methods. These mathematical formulations, based on boundary conforming grids, allow for an exact mimicking of integration-by-parts. However, other discretizations techniques that do not include one or both boundary nodes, such as pseudo-spectral collocation methods, only fulfill a generalized SBP (GSBP) property but still lead to energy-stable solutions. This thesis consists of two main topics. The first part, which is mostly devoted to theoretical investigations, treats discretizations based on SBP and GSBP operators. A numerical approximation of a conservation law is said to be conservative if the approximate solution mimics the physical conservation property. It is shown that conservative and energy-stable spatial discretizations of variable coefficient problems require an exact numerical mimicking of integration-by-parts. We also discuss the invertibility of the algebraic problems arising from (G)SBP-SAT discretizations in time of energy-stable spatial approximations. We prove that pseudo-spectral collocation methods for the time derivative lead to invertible fully-discrete problems. The same result is proved for second-, fourth- and sixth-order accurate finite-difference based time integration methods. Once the invertibility of (G)SBP-SAT discrete formulations is established, we are interested in efficient algorithms for the unique solution of such problems. To this end, the second part of the thesis has a stronger experimental flavour and deals with convergence acceleration techniques for SBP-SAT approximations. First, we consider a modified Dual Time-Stepping (DTS) technique which makes use of two derivatives in pseudo-time. The new DTS formulation, compared to the classical one, accelerates the convergence to steady-state and reduces the stiffness of the problem. Next, we investigate multi-grid methods. For parabolic problems, highly oscillating error modes are optimally damped by iterative methods, while smooth residuals are transferred to coarser grids. In this case, we show that the Galerkin condition in combination with the SBP-preserving interpolation operators leads to fast convergence. For hyperbolic problems, low frequency error modes are rapidly expelled by grid coarsening, since coarser grids have milder stability restrictions on time steps. For such problems, Total Variation Dimishing Multi-Grid (TVD-MG) allows for faster wave propagation of first order upwind discretizations. In this thesis, we extend low order TVD-MG schemes to high-order SBP-SAT upwind discretizations.