Graduate Introduction to Numerical Methods

“A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected as a notable book in computing in 2013.  Computing Reviews’ Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

• Computer Arithmetic & Fundamental Concepts of Computation.- Polynomials and Series.- Rootfinding and Function Evaluation.- Solving Ax = b .- Solving Ax =l x.- Structured Linear Systems.-Iterative Methods.- Polynomial and Rational Interpolation.- The Discrete Fourier Transform.- Numerical Integration.- Numerical Differentiation and Finite Differences.- Numerical Solution of ODEs.-  Numerical Methods for ODEs.- Numerical Solutions of Boundary Value Problems.- Numerical Solution of Delay DEs.- Numerical Solution of PDEs.​

"Corless and Fillion have clearly dedicated several years of their lives to this book. It has been worth it! The result is a carefully judged all-round numerical analysis textbook that expertly serves students and instructors. The book stands out in a crowded market. It is a textbook that numerical analysis can be very proud of." (Alex Townsend, SIAM Review, Vol. 58 (4), December, 2016) "This book is intended to be a graduate introduction to numerical methods from the perspective of backward error analysis. ... it is the variety of topics and case studies, both theoretical and numerical, presented in the book that is its strongest point, making it a valuable reference work for students and professionals ... ." (Justin Steven C. Prentice, Mathematical Reviews, January, 2015) "This textbook provides a very readable and comprehensive graduate-level introduction to numerical methods and their analysis. ... The textbook contains many references, exercises, MATLAB codes, and numerical illustrations. It is written in a style that is both informal and informative which makes this book unique in fact." (Robert Plato, zbMATH, Vol. 1295, 2014)