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finite element methods
These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various
Matrices, Moments and Quadrature with Applications
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Parallel Processing for Scientific Computing
Mathematics of Computing -- Parallelism.
Introduction to High Performance Scientific Computing
This is a textbook that teaches the bridging topics between numerical analysis, parallel computing, code performance, large scale applications.
Domain Decomposition Methods - Algorithms and Theory
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
The Lanczos and Conjugate Gradient Algorithms
The most comprehensive and up-to-date discussion available of the Lanczos and CG methods for computing eigenvalues and solving linear systems.
Numerical Methods for Least Squares Problems, Second Edition
The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to...
Computer Solution of Large Linear Systems
This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Next Generation Arithmetic
This book constitutes the refereed proceedings of the 4th International Conference on Next Generation Arithmetic, CoNGA 2023, held in Singapore, during March 1-2, 2023. The 11 full papers in this book were carefully reviewed and selected from 16 submissions. They were organized in topical sections as follows: Lossless FFTs Using Posit Arithmetic, PLAUs: Posit Logarithmic Approximate Units to Implement Low-Cost Operations with Real Numbers.
Applied and Numerical Partial Differential Equations
Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.
