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Numerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics.
Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.
This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.
As per the constant need to solve larger and larger numerical problems, it is not possible to neglect the opportunity that comes from the close adaptation of computational algorithms and their implementations for particular features of computing devices, i.e. the characteristics and performance of available workstations and servers. In the last decade, the advances in hardware manufacturing, the decreasing cost and the spread of GPUs have attracted the attention of researchers for numerical simulations, given that for some problems, GPU-based simulations can significantly outperform the ones based on CPUs. The objective of this book is first to present how to design in a context of GPGPU numerical methods in order to obtain the highest efficiency. A second objective of this book is to propose new auto-tuning techniques to optimize access on GPU. A third objective of this book is to propose new preconditioning techniques for GPGPU. Finally, an original energy consumption model is proposed, leading to a robust and accurate energy consumption prediction model. Presents step-by-step patterns for parallel programming on GPU Helps to implement efficient linear algebra operations on GPU Helps to implement efficient iterative methods on GPU Proposes new techniques to speed-up algorithms through auto-tuning on GPU Proposes new preconditioning techniques on GPU Proposed new approach to measure and to predict energy consumption of a scientific application on GPU
Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra - Detailed explanations and examples - A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Examples from engineering and science applications
Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992