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 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 for Mechanical Engineers
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
NA Pages
Numerical Methods for Computational Science and Engineering
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
839 Pages
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
NA Pages
