Introduction to Numerical ComputationAnalysis and Matlab illustrations
This ebook contains the following topics: Mathematical Models and Numerical Approximations, Numerical Computation, References, Sources of Error, Basic Concepts, Error Propagation, Number Representation, Rounding Errors in Floating Point, Arithmetic Operations in Floating Point, Accumulated Errors, IEEE Standard, Introduction, Remainder Term Estimates, Standard Functions, Range Reduction, Trigonometric Functions, Introduction, Crude Localization, Iteration Methods, Convergence Analysis, Error Estimation and StoppingCriteria, Algebraic Equations, Square Root, Nonlinear Systems, Introduction, Interpolation by Polynomials, Linear Interpolation, Lagrange Interpolation, Hermite Interpolation, Splines, Linear Spline Functions, Cubic Splines, Introduction, Richardson Extrapolation, Introduction, Trapezoidal Rule, Adaptive Quadrature, Introduction, Triangular Systems, Gaussian Elimination, Pivoting, LU Factorization, Band Matrices, Inverse Matrix, Vector and Matrix Norms, Sensitivity Analysis, Rounding Errors, Estimation of Condition Number, Overdetermined Systems, QR Factorization, Introduction, Important Concepts, Least Squares Method, Orthogonal Functions, Orthogonal Polynomials, Legendre Polynomials, Chebyshev Polynomials, Discrete Cosine Transform, Minimax Approximation, Introduction, Initial Value Problems, Local and Global Error, An Implicit Method, Stability, Adaptive Step Length Control, Boundary Value Problems, A Finite Element Method, The Shooting Method, Mathematical Models and Numerical Approximations
Author(s): Lars Elden Linde Wittmeyer-Koch Hans Bruun Nielsen
383 Pages 
Introduction to Numerical Computation
This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch, and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to numerical computation. The text begins with the basics like error analysis and computer arithmetic, which gives a very solid ground for the origin and handling of numerical errors. It proceeds further to explain more basic topics related to function evaluation, solutions of nonlinear equations, and interpolation techniques. Next, it describes procedures for improving numerical estimates using differentiation and Richardson extrapolation. This is followed by full details of integration, systems of linear equations, and approximation. Finally, ordinary differential equations complete a thorough course of study that will prepare the reader with both the theory and practice that will serve in carrying out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans Bruun Nielsen
383 Pages
Numerical Computation UniOviedo
This PDF is prepared by Gonzalo Galiano Casas and Esperanza Garcia Gonzalo from the Department of Mathematics at Oviedo University. With a view to keeping things compact, this document initiates with finite arithmetic and error analysis, which forms the basis necessary for understanding the issue of numerical precision and limitations. It considers methods for nonlinear equations, interpolation, and approximation. Key sections on numerical differentiation and integration give hands-on tools both for data analysis and the solution of mathematical problems. It also covers systems of linear equations and optimization, rounding it out for students and practitioners who might want to apply the numerical methods through a variety of problems.
Author(s): Gonzalo Galiano Casas, Esperanza Garcia Gonzalo, Dept. of Mathematics, Oviedo University
114 Pages
Prof. L. Vandenberghe's lecture note is on applied numerical computing but brings out the practical application aspect. The text covers most areas of numerical linear algebra, nonlinear optimization nonlinear least squares, introduction to floating-point numbers, and rounding errors that are to be needed for understanding the issues of numerical precision. Examples are drawn from signal and image processing, control systems, and machine learning, among other areas, to indicate how these numerical methods are actually applied. This resource aims to fill the gap between theory and practice by providing a practical method for solving computational problems.
Author(s): Prof. L. Vandenberghe
NA Pages
Lectures in Basic Computational Numerical Analysis (PDF 168P)
This lecture series provides comprehensive foundational knowledge in the field of numerical computational analysis. Numerical Linear Algebra covers basic matrix operations and solutions of linear systems. The book further goes into the Solution of Nonlinear Equations that shows methods for solving equations which are not linear in form. Finally, it discusses Approximation Theory, showing how functions and data may be approximated. The lectures also cover Numerical Solution of ODEs and PDEs, giving ways to solve these two basic kinds of equations. This resource is intended for students and professionals looking to gain a solid understanding of basic and applied numerical analysis techniques.
Author(s): J. M. McDonough
168 Pages
