This textbook is a concise introduction to the fundamental concepts and methods of numerical mathematics. The author manages to cover the many important topics while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science. In general, the author assumes only a knowledge of calculus and linear algebra.
The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis.
The book first examines high-order classical integration methods from the structure preservation point of view.
This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis.
Exercise. Consider the linear system of equations Ax = b for the matrix A = 1 v u I ∈ K m×m . • Permute the rows and columns of A in such a way that the storage cost for the factors of an LU decomposition grows just ...
[63] Langville, A. and C. Meyer (2004). Deeper inside PageRank. Internet Mathematics 1(3), 335–380. [64] Langville, A. and C. Meyer (2006). Google's PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press.
In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms.
With brevity, precision, and rigor, the work is an ideal choice for a standard one-semester course targeted primarily at math or physics majors. It is a valuable addition to the book collection of anyone who teaches or studies the subject.
An Introduction to the Gradient Discretisation Method Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin Abstract We show that three classical examples of schemes for the approximation of linear ...
This little book is the outgrowth of a one semester course which I have taught for each of the past four years at M. 1.
Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful.