A concise introduction to numerical analysis. (2016)

• Record Type: Book
• Further Information: Note: A.C. Faul.
• Authors: Faul, A. C (Anita C.)
• Contents: Fundamentals; Floating Point Arithmetic; Overflow and Underflow; Absolute, Relative Error, Machine Epsilon; Forward and Backward Error Analysis; Loss of Significance; Robustness; Error Testing and Order of Convergence; Computational Complexity; Condition; Revision Exercises; ; Linear Systems; Simultaneous Linear Equations; Gaussian Elimination and Pivoting; LU Factorization; Cholesky Factorization; QR Factorization; The Gram–Schmidt Algorithm; Givens Rotations; Householder Reflections; Linear Least Squares; Singular Value Decomposition; Iterative Schemes and Splitting; Jacobi and Gauss–Seidel Iterations; Relaxation; Steepest Descent Method; Conjugate Gradients; Krylov Subspaces and Pre-Conditioning; Eigenvalues and Eigenvectors; The Power Method; Inverse Iteration; Deflation; Revision Exercises; ; Interpolation and Approximation Theory; Lagrange Form of Polynomial Interpolation; Newton Form of Polynomial Interpolation; Polynomial Best Approximations; Orthogonal polynomials; Least-Squares Polynomial Fitting; The Peano Kernel Theorem; Splines; B-Spline; Revision Exercises; ; Non-Linear Systems; Bisection, Regula Falsi, and Secant Method; Newton’s Method; Broyden’s Method; Householder Methods; Müller’s Method; Inverse Quadratic Interpolation; Fixed Point Iteration Theory; Mixed Methods; Revision Exercises; ; Numerical Integration; Mid-Point and Trapezium Rule; The Peano Kernel Theorem; Simpson’s Rule; Newton–Cotes Rules; Gaussian Quadrature; Composite Rules; Multi-Dimensional Integration; Monte Carlo Methods; Revision Exercises; ; ODEs; One-Step Methods; Multistep Methods, Order, and Consistency; Order Conditions; Stiffness and A-Stability; Adams Methods; Backward Differentiation Formulae; The Milne and Zadunaisky Device; Rational Methods; Runge–Kutta Methods; Revision Exercises; ; Numerical Differentiation; Finite Differences; Differentiation of Incomplete or Inexact Data; ; PDEs; Classification of PDEs; Parabolic PDEs; Elliptic PDEs; Parabolic PDEs in Two Dimensions; Hyperbolic PDEs; Spectral Methods; Finite Element Method; Revision Exercises
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 518; Numerical analysis
• Languages: English
• ISBNs: 9781498712217; 9781498712194; 9781498712200
• Related ISBNs: 9781498712187
• Notes: Note: Includes bibliographical references and index.; 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.