Numerical Analysis

e-books in Numerical Analysis category

Numerical Methods for Large Eigenvalue Problems
by Yousef Saad , 2011
A comprehensive guide to computational techniques for finding eigenvalues and eigenvectors of large matrices. It emphasizes practical algorithms and software development, particularly for sparse matrices. The book covers background theory ...
(1520 views)

First Semester in Numerical Analysis with Julia
by Giray Ökten - Florida State University , 2019
The book presents the theory and methods, together with the implementation of the algorithms using the Julia programming language. The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory.
(8104 views)

Geometric Transformation of Finite Element Methods: Theory and Applications
by M. Holst, M. Licht - arXiv.org , 2018
We present a new technique to apply finite element methods to partial differential equations over curved domains. Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove finite element convergence rates for the problem.
(6931 views)

Programming for Computations - Python
by Svein Linge, Hans Petter Langtangen - Springer , 2016
This book presents Python programming as a key method for solving mathematical problems. The style is accessible and concise, the emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
(11409 views)

Finite Difference Computing with PDEs
by Hans Petter Langtangen, Svein Linge - Springer , 2017
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners.
(7569 views)

Solving PDEs in Python
by Hans Petter Langtangen, Anders Logg - Springer , 2017
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, it guides readers through the essential steps to quickly solving a PDE in FEniCS.
(8092 views)

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics
by Justin Solomon - CRC Press , 2015
Using examples from a broad base of computational tasks, including data processing and computational photography, the book introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into theoretical tools.
(11698 views)

Introduction to Numerical Methods and Matlab Programming for Engineers
by Todd Young, Martin J. Mohlenkamp - Ohio University , 2017
The goals of these notes are to introduce concepts of numerical methods and introduce Matlab in an Engineering framework. The notes were developed by the author in the process of teaching a course on applied numerical methods for Civil Engineering.
(8328 views)

Introduction to Numerical Methods
by Jeffrey R. Chasnov - The Hong Kong University , 2012
This is primarily for non-mathematics majors and is required by several engineering departments. Contents: IEEE Arithmetic; Root Finding; Systems of equations; Least-squares approximation; Interpolation; Integration; Ordinary differential equations.
(10828 views)

Scientific Computing
by Jeffrey R. Chasnov - Harvey Mudd College , 2013
This course consists of both numerical methods and computational physics. MATLAB is used to solve various computational math problems. The course is primarily for Math majors and supposes no previous knowledge of numerical analysis or methods.
(10041 views)

The Numerical Approximation of Functional Differential Equations
by Daniele Venturi - arXiv , 2016
The purpose of this manuscript is to provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
(8666 views)

Tea Time Numerical Analysis
by Leon Q. Brin - Southern Connecticut State University , 2014
A one semester introduction to numerical analysis. Includes typical introductory material, root finding, numerical calculus, and interpolation techniques. The focus is on the mathematics rather than application to engineering or sciences.
(11166 views)

Computing of the Complex Variable Functions
by Solomon I. Khmelnik, Inna S. Doubson - MiC , 2011
Hardware algorithms for computing of all elementary complex variable functions are proposed. Contents: A method 'digit-by-digit'; Decomposition; Compositions; Two-step-by-step operations; Taking the logarithm; Potentiation; and more.
(10963 views)

Parallel Spectral Numerical Methods
by Gong Chen, et al. - Wikibooks , 2013
We start with finite-precision arithmetic. We then discuss how to solve ordinary differential equations and partial differential equations using the technique of separation of variables. We then introduce numerical time-stepping schemes...
(10187 views)

Numerical Solutions of Engineering Problems
by K. Nandakumar - University of Alberta , 1998
Contents: On mathematical models; Single nonlinear algebraic equation; System of linear and nonlinear algebraic equations; Numerical differentiation and integration; Ordinary differential equations; Boundary value problems; etc.
(17927 views)

Lectures on Numerical Methods in Bifurcation Problems
by H.B. Keller - Tata Institute Of Fundamental Research , 1986
These lectures introduce the modern theory and practical numerical methods for continuation of solutions of nonlinear problems depending upon parameters. The treatment is elementary, advanced calculus and linear algebra are the omly prerequisites.
(10354 views)

Lectures on Numerical Methods for Non-Linear Variational Problems
by R. Glowinski - Tata Institute of Fundamental Research , 1980
Many physics problems have variational formulations making them appropriate for numerical treatment. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations.
(11876 views)

Lectures on Topics In Finite Element Solution of Elliptic Problems
by Bertrand Mercier - Tata Institute of Fundamental Research , 1979
Contents: Sobolev Spaces; Abstract Variational Problems and Examples; Conforming Finite Element Methods; Computation of the Solution of the Approximate Problem; Problems with an Incompressibility Constraint; Mixed Finite Element Methods; etc.
(10919 views)

Numerical Methods For Time Dependent Equations
by P. Lascaux - Tata Institute of Fundamental Research , 1976
The solution of time dependent equations of hydrodynamics is a subject of great importance. This book is mainly concentrated on the study of the stability of the various schemes. We have considered only the stability for linearized problems.
(11484 views)

Lectures on The Finite Element Method
by Ph. Ciarlet - Tata Institute of Fundamental Research , 1975
Our basic aim has been to present some of the mathematical aspects of the finite element method, as well as some applications of the finite element method for solving problems in Elasticity. This is why some important topics are not covered here.
(11928 views)

Numerical Analysis I
by Mark Embree - Rice University , 2012
This course takes a tour through many algorithms of numerical analysis. We aim to assess alternative methods based on efficiency, to discern well-posed problems from ill-posed ones, and to see these methods in action through computer implementation.
(15959 views)

Iterative Methods for Linear and Nonlinear Equations
by C.T. Kelley - SIAM , 1995
This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods.
(13155 views)

Numerical Methods for Large Eigenvalue Problems
by Yousef Saad - SIAM , 2011
This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods for solving matrix eigenvalue problems that arise in various engineering applications.
(16439 views)

Numerical Analysis for Engineering
by Douglas W. Harder, Richard Khoury - University of Waterloo , 2010
Contents: Error Analysis, Numeric Representation, Iteration, Linear Algebra, Interpolation, Least Squares, Taylor Series, Bracketing, The Five Techniques, Root Finding, Optimization, Differentiation, Integration, Initial-value Problems, etc.
(15562 views)

Numerical Analysis: Theory and Application
by Jan Awrejcewicz - InTech , 2011
The book introduces theoretical approach to numerical analysis as well as applications of various numerical methods to solving numerous theoretical and engineering problems. The book is useful for both theoretical and applied research.
(13194 views)

Lectures on Numerical Analysis
by Dennis Deturck, Herbert S. Wilf - University of Pennsylvania , 2002
Contents: Differential and Difference Equations (Linear equations with constant coefficients, Difference equations, Stability theory); The Numerical Solution of Differential Equations (Euler's method); Numerical linear algebra.
(13610 views)

Notes on Numerical Linear Algebra
by George Benthien , 2006
Tutorial describing many of the standard numerical methods used in Linear Algebra. Topics include Gaussian Elimination, LU and QR Factorizations, The Singular Value Decomposition, Eigenvalues and Eigenvectors via the QR Method, etc.
(16360 views)

Notes on Harmonic Analysis
by George Benthien , 2006
Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.
(12778 views)

Robust Geometric Computation
by Kurt Mehlhorn, Chee Yap - New York University , 2004
Contents: Introduction to Geometric Nonrobustness; Modes of Numerical Computation; Geometric Computation; Arithmetic Approaches; Geometric Approaches; Exact Geometric Computation; Perturbation; Filters; Algebraic Background; Zero Bounds; etc.
(12460 views)

Numerical Stability
by M.N. Spijker - Leiden University , 1998
Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.
(11930 views)

Introduction to the Numerical Integration of PDEs
by B. Piette - University of Durham , 2004
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
(14516 views)

The Calculus Of Finite Differences
by L. M. Milne Thomson - Macmillan and co , 1933
The object of this book is to provide a simple account of the subject of Finite Differences and to present the theory in a form which can be readily applied -- not only the useful material of Boole, but also the more modern developments.
(16953 views)

Introduction to Fortran 95 and Numerical Computing
by Adrian Sandu - Virginia Tech , 2001
Contents: a quick tour of fortran 95; the building blocks of a fortran application; flow control; computer arithmetic; applications; intrinsic functions; input and output; arrays; more on procedures; parametrized intrinsic types; derived types; etc.
(14640 views)

Computational Mathematics for Differential Equations
by N. V. Kopchenova, I. A. Maron , 1975
This is a manual on solving problems in computational mathematics. The book is intended primarily for engineering students, but may also prove useful for economics students, graduate engineers, and postgraduate students in the applied sciences.
(20082 views)

Iterative Methods for Sparse Linear Systems
by Yousef Saad - PWS , 1996
The book gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
(13098 views)

First Steps in Numerical Analysis
by R. Hosking, S. Joe, D. Joyce, and J. Turner , 1998
This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The subject matter is organized into fundamental topics and presented as a series of steps.
(16907 views)

Lectures in Basic Computational Numerical Analysis
by James M. McDonough - University of Kentucky , 2001
These notes cover the following topics: Numerical linear algebra; Solution of nonlinear equations; Approximation theory; Numerical solution of ordinary differential equations; Numerical solution of partial differential equations.
(13803 views)

Numerical Recipes in Fortran 90
by William H. Press, at al. - Cambridge University Press , 1996
Numerical Recipes in Fortran 90 contains a detailed introduction to the Fortran 90 language and to the basic concepts of parallel programming, plus source code for all routines from the second edition of Numerical Recipes.
(21015 views)

Handbook of Mathematical Functions
by M. Abramowitz, I. A. Stegun - GPO , 1964
Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for special functions, standard trig, and exponential logarithmic definitions and extensions.
(35078 views)

Mathematical Computation
by Ian Craw - University of Aberdeen , 2003
The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work.
(16173 views)

Numerical Methods Course Notes
by Steven E. Pav - University of California at San Diego , 2005
From the table of contents: A 'Crash' Course in octave/Matlab; Solving Linear Systems; Finding Roots; Interpolation; Spline Interpolation; Approximating Derivatives; Integrals and Quadrature; Least Squares; Ordinary Differential Equations.
(16988 views)

Fundamental Numerical Methods and Data Analysis
by George W. Collins, II - NASA ADS , 2003
'Fundamental Numerical Methods and Data Analysis' can serve as the basis for a wide range of courses that discuss numerical methods used in science. The author provides examples of the more difficult algorithms integrated into the text.
(19587 views)

Numerical Methods with Applications
by Autar K Kaw, Egwu Eric Kalu - Lulu.com , 2008
The textbook is written for engineering undergraduates taking a course in numerical methods. It offers a treatise to numerical methods based on a holistic approach and short chapters. The authors included examples of real-life applications.
(22632 views)

Templates for the Solution of Linear Systems
by Richard Barrett et al. - Society for Industrial Mathematics , 1987
The book focuses on the use of iterative methods for solving large sparse systems of linear equations. General and reusable templates are introduced to meet the needs of both the traditional user and the high-performance specialist.
(18092 views)