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Languages : en
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Author: Richard Barrett
Publisher: SIAM
ISBN: 0898713285
Category : Mathematics
Languages : en
Pages : 130
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Andrew John Sommese
Publisher: World Scientific
ISBN: 9812561846
Category : Mathematics
Languages : en
Pages : 425
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Book Description
Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.
Author: Charles K Chui
Publisher: World Scientific
ISBN: 981454907X
Category : Mathematics
Languages : en
Pages : 454
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Book Description
This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
Author: James W. Demmel
Publisher: SIAM
ISBN: 0898713897
Category : Mathematics
Languages : en
Pages : 426
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Book Description
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author: Siham Tabik
Publisher: Universidad Almería
ISBN: 8482408844
Category : Computers
Languages : en
Pages : 156
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Book Description
La mayoría de los modelos matemáticos empleados para describir fenómenos físicos reales en ciencia e ingeniería están gobernados por ecuaciones parciales diferenciales no-lineales dependientes del tiempo PDEs (Partial Differential Equations). Generalmente, la solución de dichas ecuaciones requiere una discretización usando métodos como los de diferencias finitas, elementos finitos, volúmenes finitos o métodos de los momentos. El análisis del comportamiento de los modelos matemáticos basados en PDEs para sistemas reales es muy costoso desde el punto de vista computacional, y los costes pueden ser tan enormes que su implementación paralela se convierte en la única solución. Adicionalmente, la reciente disponibilidad en el mercado de la computación de alta prestación de arquitecturas de nodos de memoria compartida conectados entre si ha incrementado la importancia de diseñar códigos eficientes apropiados para explotar estas plataformas. Dichas plataformas soportan tres paradigmas de comunicación: 1) el paradigma de memoria compartida, 2) el paradigma de paso de mensajes, y 3) el paradigma híbrido, que consiste en la combinación de los dos paradigmas anteriores. Cada uno de los paradigmas ofrece ventajas y desventajas en función de las características de la plataforma paralela y del problema. Esta tesis analiza la solución numérica de tres aplicaciones científicas en física y en el campo del tratamiento de imágenes gobernadas por ecuaciones diferenciales, tridimensionales, independientes del tiempo. En particular, la primera aplicación es un método dependiente del tiempo que resuelve la ecuación integral del campo eléctrico para el análisis de la interacción entre hilos finos conductores y ondas electromagnéticas; la segunda aplicación es un método de diferencias finitas que resuelve la ecuación de difusión altamente acoplada con un sistemas masivo para filtrar imágenes 3D en biología celular y biomedicina; y la tercera aplicación es un conjunto de cuatro ecuaciones de reacción-difusión para simular el fenómeno de bursting en tres dimensiones, un fenómeno común en numerosos sistemas naturales. Para ello, se analizan las características de los paradigmas de comunicación conforme se aplican para obtener las soluciones numéricas de las tres aplicaciones descritas anteriormente. Los resultados indican que es posible establecer una abstracción de los modelos de comunicación que permite un desarrollo eficiente, simple y robusto de los modelos de comunicación que son independientes de las arquitecturas de las diferentes plataformas usadas.
Author: Arieh Iserles
Publisher: Cambridge University Press
ISBN: 9781107043862
Category : Mathematics
Languages : en
Pages : 580
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Book Description
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
Author: Eugene L. Allgower
Publisher: SIAM
ISBN: 089871544X
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.
Author: Gerhard Zumbusch
Publisher: Springer Science & Business Media
ISBN: 3322800636
Category : Mathematics
Languages : en
Pages : 215
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Book Description
Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.
Author: Roland Glowinski
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110785013
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This text on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to split complicated computational fluid dynamics problems into a sequence of simpler sub-problems. A methodology for solving more advanced applications such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid is also presented.
