Numerical Methods and Optimization

From Calculus to Computation.- Notation and Norms.- Solving Systems of Linear Equations.- Solving Other Problems in Linear Algebra.- Interpolation and Extrapolation.- Integrating and Differentiating Functions.- Solving Systems of Nonlinear Equations.- Introduction to Optimization.- Optimizing Without Constraint.- Optimizing Under Constraints.- Combinatorial Optimization.- Solving Ordinary Differential Equations.- Solving Partial Differential Equations.- Assessing Numerical Errors.- WEB Resources to go Further.- Problems.

"The book discusses the numerical methods most frequently used by scientists and engineers. It is well organized, clearly written, and has a large amount of concrete details/examples that are extremely useful for practice. ... Each chapter contains its own list of references, as well as a final section that summarizes the key issues of the chapter." (Octavian Pastravanu, zbMATH 1328.65006, 2016)

"This book is all about the know-how of numerical analysis. If you want to implement numerical procedures and fancy the help of someone who knows what usually happens when something goes wrong, knows how to fix it, and can provide rules of thumb to deal with most of the situations encountered in practice, this book is made for you." (Gérard Lebourg, Mathematical Reviews, August, 2015)

"This work is a reference on methods for numerical computation and optimization. ... This book may be a useful resource for advanced students and researchers in a wide range of engineering and science disciplines. Summing Up: Recommended. Graduate students and researchers/faculty." (B. Borchers, Choice, Vol. 52 (5), January, 2015)

"This is a very erudite survey of numerical methods. ... The book teaches you how to analyze your problem and pick the best numerical method to solve it. It covers all the standard areas of numerical analysis." (Allen Stenger, MAA Reviews, November, 2014)