LAPACK Users' Guide, 3rd Edition

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

Numerical Computation by Peter Bastian

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

236 Pages

Applied Numerical Computing

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

Numerical Methods for Scientific Computing

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

NA Pages