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Books in Numerical analysis

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11-20 of 70 results in All results

Convexity Theory and its Applications in Functional Analysis

  • 1st Edition
  • June 28, 2014
  • L. Asimow
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 4 6 9 - 8
Convexity Theory and its Applications in Functional Analysis is a five-chapter text that provides a geometric perspective of the convexity theory and its practical applications. Chapter 1 reviews the functional analytic preliminaries, including the Krein-Smulyan Theorem, the basic Choquet Theory, and the Bishop-Phelps Theorem. Chapter 2 gives the basic duality results, lattice theory and concrete representation theorems for order unit spaces and Banach lattices of type Mand L. Chapters 3 and 4 deal with the real affine function spaces through examining the Choquet simplex and the application of the study of real A(K) spaces to complex-values function spaces by means of a complex state space. Chapter 5 highlights the application of the theory to the study of non-commutative Banach algebras. This book will prove useful to mathematicians, engineers, and physicists.

Scientific Computing

  • 1st Edition
  • June 28, 2014
  • Gene H. Golub + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 6 0 4 - 3
This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

Numerical Mathematics and Applications

  • 1st Edition
  • Volume 1
  • June 28, 2014
  • J. Vignes + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 5 6 7 - 1
IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on August 5-9, 1985. The book focuses on the processes, methodologies, and approaches involved in computer arithmetic. The selection first highlights the use of CESTAC method in the parallel computation of roots of polynomials, CESTAC, and reducing abbreviation errors in iterative resolution of linear systems. Discussions focus on notations and theoretical processes, sequence of iterates in floating-point arithmetic, perturbation method, and CESTAC tested on algorithm and numerical results. The book then takes a look at optimal termination criterion and accuracy tests in mathematical programming; use of the normed residue to check the quality of the solution of a linear system; and computable bounds for solutions of integral equations. The manuscript examines arbitrarily accurate boundaries for solutions of ODEs with initial values using variable precision arithmetic and remarks on some modified Romberg algorithms for numerical integration. Topics include speed of convergence and a priori truncation error estimates, acceleration of convergence, extrapolation schemes, and the initial boundary value problem. The selection is a dependable source of data for mathematicians and researchers interested in numerical mathematics and applications.

Computational Methods in Nonlinear Structural and Solid Mechanics

  • 1st Edition
  • May 20, 2014
  • Ahmed K. Noor + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 5 6 4 - 8
Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Numerical Methods in Software and Analysis

  • 2nd Edition
  • May 19, 2014
  • John R. Rice
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 5 6 8 - 8
Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem—there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms. The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts.

Applied Nonlinear Analysis

  • 1st Edition
  • May 12, 2014
  • V. Lakshmikantham
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 7 2 0 6 - 1
Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

An Introduction to Numerical Mathematics

  • 1st Edition
  • May 12, 2014
  • Eduard L. Stiefel
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 2 5 4 1 - 8
An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

An Introduction to Nonsmooth Analysis

  • 1st Edition
  • November 26, 2013
  • Juan Ferrera
  • English
  • Paperback
    9 7 8 - 0 - 1 2 - 8 0 0 7 3 1 - 0
  • eBook
    9 7 8 - 0 - 1 2 - 8 0 0 8 2 5 - 6
Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.

Numerical Methods for Roots of Polynomials - Part II

  • 1st Edition
  • Volume 16
  • July 19, 2013
  • J.M. McNamee + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 3 1 4 3 - 2
Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.

The Numerical Method of Lines

  • 1st Edition
  • July 27, 2012
  • William E. Schiesser
  • English
  • eBook
    9 7 8 - 0 - 1 2 - 8 0 1 5 5 1 - 3
This is the first book on the numerical method of lines, a relatively new method for solving partial differential equations. The Numerical Method of Lines is also the first book to accommodate all major classes of partial differential equations. This is essentially an applications book for computer scientists. The author will separately offer a disk of FORTRAN 77 programs with 250 specific applications, ranging from "Shuttle Launch Simulation" to "Temperature Control of a Nuclear Fuel Rod."