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Fundamentals of Matrix Computations (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

Fundamentals of Matrix Computations (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) Lowest new price: $50.16
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Author: David S. Watkins

This new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computing

Retaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.

Along with new and updated examples, the Third Edition features:

  • A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm
  • Application of classical Gram-Schmidt with reorthogonalization
  • A revised approach to the derivation of the Golub-Reinsch SVD algorithm
  • New coverage on solving product eigenvalue problems
  • Expanded treatment of the Jacobi-Davidson method
  • A new discussion on stopping criteria for iterative methods for solving linear equations

Throughout the book, numerous new and updated exercises—ranging from routine computations and verifications to challenging programming and proofs—are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.

Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper-undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.

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Topics in Matrix Analysis

Topics in Matrix Analysis Lowest new price: $57.66
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Author: Roger A. Horn

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work.

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Iterative Methods for Sparse Linear Systems, Second Edition

Iterative Methods for Sparse Linear Systems, Second Edition Lowest new price: $87.93
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Author: Yousef Saad

Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of linear and nonlinear systems arising in typical applications has grown, meaning that using direct solvers for the three-dimensional models of these problems is no longer effective. At the same time, parallel computing, becoming less expensive and standardized, has penetrated these application areas. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best methods available today. A new chapter on multigrid techniques has been added, whilst material throughout has been updated, removed or shortened. Numerous exercises have been added, as well as an updated and expanded bibliography.

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Matrix Mathematics: Theory, Facts, and Formulas (Second Edition)

Matrix Mathematics: Theory, Facts, and Formulas (Second Edition) Lowest new price: $44.98
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Author: Dennis S. Bernstein

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.

Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms.

  • Covers hundreds of important and useful results on matrix theory, many never before available in any book
  • Provides a list of symbols and a summary of conventions for easy use
  • Includes an extensive collection of scalar identities and inequalities
  • Features a detailed bibliography and author index with page references
  • Includes an exhaustive subject index with cross-referencing

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An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics) Lowest new price: $44.58
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Author: Greg W. Anderson

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

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Linear Algebra and Matrix Theory

Linear Algebra and Matrix Theory Lowest new price: $92.80
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Author: E. D. Nering

This revision of a well-known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, and the concept of duality receives expanded coverage. Notations have been changed to correspond to more current usage.

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GNU Octave Manual Version 3

GNU Octave Manual Version 3 Lowest new price: $26.21
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Author: John W Eaton

This manual is the definitive guide to GNU Octave, an interactive environment for numerical computation. GNU Octave provides a convenient command-line interface for solving linear and nonlinear problems using vectors and matrices. This updated edition of the manual covers version 3 of GNU Octave, and includes documentation for new features such as sparse matrices, linear programming and computational geometry. GNU Octave is free software, distributed under the GNU General Public License (GPL). All the money raised from the sale of this book supports the development of free software. For each copy sold $1 will be donated to the GNU Octave Development Fund. About the authors: John W. Eaton is the original developer of GNU Octave.

Features:

  • ISBN13: 9780954612061
  • Condition: New
  • Notes: BRAND NEW FROM PUBLISHER! 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!

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Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences)

Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences) Lowest new price: $13.40
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Author: Krishnan Namboodiri

Matrix Algebra is a vital tool for mathematics in the social sciences, and yet many social scientists have only a rudimentary grasp of it. This volume serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. Namboodiri's presentation is smooth and readable: it begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors -- supplying illustrations through fully-worked examples.

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Matrix Groups for Undergraduates (Student Mathematical Library,)

Matrix Groups for Undergraduates (Student Mathematical Library,) Lowest new price: $29.67
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Author: Kristopher Tapp

Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory.

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Optimization Algorithms on Matrix Manifolds

Optimization Algorithms on Matrix Manifolds Lowest new price: $48.34
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Author: P.-A. Absil

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.

Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

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