Numerical analysis with algorithms and programming. (2016)

• Record Type: Book
• Further Information: Note: Santanu Saha Ray.
• Authors: Saha Ray, Santanu
• Contents: Errors in Numerical Computations; Introduction; Preliminary Mathematical Theorems; Approximate Numbers and Significant Figures; Rounding Off Numbers; Truncation Errors; Floating Point Representation of Numbers; Propagation of Errors; General Formula for Errors; Loss of Significance Errors; Numerical Stability, Condition Number, and Convergence; Brief Idea of Convergence Numerical Solutions of Algebraic and Transcendental Equations ; Introduction; Basic Concepts and Definitions; Initial Approximation; Iterative Methods; Generalized Newton’s Method; Graeffe’s Root Squaring Method for Algebraic Equations Interpolation ; Introduction; Polynomial Interpolation Numerical Differentiation ; Introduction; Errors in Computation of Derivatives; Numerical Differentiation for Equispaced Nodes; Numerical Differentiation for Unequally Spaced Nodes; Richardson Extrapolation Numerical Integration ; Introduction; Numerical Integration from Lagrange’s Interpolation; Newton–Cotes Formula for Numerical Integration (Closed Type); Newton–Cotes Quadrature Formula (Open Type); Numerical Integration Formula from Newton’s Forward Interpolation Formula; Richardson Extrapolation ; Romberg Integration; Gauss Quadrature Formula; Gaussian Quadrature: Determination of Nodes and Weights through Orthogonal Polynomials; Lobatto Quadrature Method; Double Integration; Bernoulli Polynomials and Bernoulli Numbers; Euler–Maclaurin Formula Numerical Solution of System of Linear Algebraic Equations ; Introduction; Vector and Matrix Norm; Direct Methods; Iterative Method; Convergent Iteration Matrices; Convergence of Iterative Methods; Inversion of a Matrix by the Gaussian Method; Ill-Conditioned Systems; Thomas Algorithm Numerical Solutions of Ordinary Differential Equations ; Introduction; Single-Step Methods; Multistep Methods; System of Ordinary Differential Equations of First Order; Differential Equations of Higher Order; Boundary Value Problems; Stability of an Initial Value Problem; Stiff Differential Equations; A-Stability and L-Stability Matrix Eigenvalue Problem ; Introduction; Inclusion of Eigenvalues; Householder’s Method; The QR Method; Power Method; Inverse Power Method; Jacobi’s Method; Givens Method Approximation of Functions ; Introduction; Least Square Curve Fitting; Least Squares Approximation; Orthogonal Polynomials; The Minimax Polynomial Approximation; B-Splines; Padé Approximation Numerical Solutions of Partial Differential Equations ; Introduction; Classification of PDEs of Second Order; Types of Boundary Conditions and Problems; Finite-Difference Approximations to Partial Derivatives; Parabolic PDEs; Hyperbolic PDEs; Elliptic PDEs; Alternating Direction Implicit Method; Stability Analysis of the Numerical Schemes An Introduction to the Finite Element Method; Introduction; Piecewise Linear Basis Functions; The Rayleigh–Ritz Method; The Galerkin Method Bibliography Answers Index Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 518; Numerical analysis -- Problems, exercises, etc; Engineering mathematics -- Problems, exercises, etc; Numerical analysis -- Data processing -- Problems, exercises, etc; Algorithms -- Problems, exercises, etc
• Languages: English
• ISBNs: 9781498741835; 9781498741767; 9781498741828
• Related ISBNs: 9781498741743
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.