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
383Pages
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
114Pages
Numerical Topics in Fluid Dynamics Computation!!! Peter Bastian Authored - This PDF covers advanced numerical computation topics but puts more emphasis on the solution of computational fluid dynamics. The book starts with the modeling of immiscible fluid flow in a composite porous medium, thus laying down the basics for the equations of multiphase fluid flow. It then provides fully implicit methods that have been used to find the finite volume discretization of systems for complex algebraic equations. Two important chapters are the parallelization methods that result in higher productivity of computation and the UG framework used for carrying out grid computations. Numerical results are then presented, which allow deriving some conclusions concerning practical applications and performance. The document will be particularly useful to researchers and engineers studying computational fluid dynamics and related numerical modeling problems.
Author(s): Peter Bastian
236Pages
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
NAPages
This note introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation, integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches.
Author(s): Prof. Anthony T. Patera, Prof. Daniel Frey and Prof. Nicholas Hadjiconstantinou
NAPages
The resource described here is an overview of numerical methods important in the study of computational science and engineering. The text starts off with Computing with Matrices and Vectors, foundational elements in many algorithms. The note moves forward and explains Direct Methods for Linear Systems of Equations and Direct Methods for Linear Least Squares Problems, important problem-solving aspects in linear algebra. The Filtering Algorithms for data processing are reviewed, while Data Interpolation and Data Fitting in 1D discuss ways of approximating onedimensional data. Approximation of Functions in 1D and Numerical Quadrature introduce the techniques on function approximation and integration. It also discusses Iterative Methods for Non-Linear Systems of Equations and Eigenvalues-a critical topic needed for solving complex systems. It finally includes Numerical Integration and Structure Preserving Integration, fundamental to perform numerical calculations with appropriate accuracy in scientific computing.
Author(s): Prof. R. Hiptmair
839Pages
This book is a technical reference to the floating-point environment supported on SPARCTM and x86 platforms running under the Solaris operating system. The book describes the Floating-Point Environment, the representation and computation of floating point numbers and how the results of arithmetic operations are rounded. The Software and Hardware Support section describes how numerical operations are passed between the hardware and software of the system. The book should be indispensable to anyone seeking an understanding of how numerical computations are executed and optimized on Solaris systems. In particular, it will be an asset worth having in real life for developers and engineers working in the field of numerical algorithms within this particular environment of computing and offers a deep view into performance and accuracy considerations.
Author(s): Sun microsystems
NAPages
It gives an explanation of all the different numerical methods of scientific computing. It starts with the basics, which is Root Finding and Orthogonal Functions, solving equations and analyzing functions. Finite Differences and Divided Differences included for the needs in the process of numerical differentiation and interpolation. Interpolation and Curve Fitting are given to outline estimation and modeling. It also includes Z-Transforms and Summation Formulas for signal processing and numerical summation. Quadrature Formulas and Ordinary Differential Equations are explained for integration and the solution of differential equations. Partial Differential Equations, Integral Equations, and Stability and Error Analysis form the advanced topics for numerical methods coverage. Further, Monte Carlo Techniques, Message Passing Interface, and Simulation Modeling are included to point out methods for probabilistic simulations and parallel computing.
Author(s): John Henry Heinbockel
NAPages
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
168Pages
