Numerical analysis Books

Most books on algorithms are narrowly focused on a single field of application. This unique book cuts across discipline boundaries, exposing readers to the most successful algorithms from a variety of fields. Algorithm derivation is a legitimate branch...

This book discusses the foundations of the mathematical theory of finite element methods. The focus is on the concept of discrete stability and the exact sequence conforming elements and covers both coercive and non-coercive problems. Following a...

Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to...

Rounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices. A detailed analysis is given of the rounding errors made in the...

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their...

Fit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems. Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides...

Applied Numerical Linear Algebra introduces students to numerical issues that arise in linear algebra and its applications. A wide range of techniques are touched on, including direct to iterative methods, orthogonal factorizations, least squares,...

Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and...

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve...

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve...

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available...

This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice Rene Frechet. Hadamard semidifferential calculus is possibly the...

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This...

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving...

This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems-interpolation, integration, linear...

This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT)...

Scientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the...