Numerical Methods and Optimization: A Consumer Guide

ISBN-13: 9783319076706 / Angielski / Twarda / 2014 / 476 str.

Eric Walter

Opis

Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods - a Consumer Guide presents methods for dealing with them.Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to - discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems;- understand the principles behind recognized algorithms used in state-of-the-art numerical software;- learn the advantages and limitations of these algorithms, to facilitate the choice of which pre-existing bricks to assemble for solving a given problem; and- acquire methods that allow a critical assessment of numerical results. Numerical Methods - a Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied mathematics.

Recenzje

"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)

Spis treści

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.

Blurb

Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them.

Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to

·         discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems;

·         understand the principles behind recognized algorithms used in state-of-the-art numerical software;

<·         learn the advantages and limitations of these algorithms, to facilitate the choice of which pre-existing bricks to assemble for solving a given problem; and

·         acquire methods that allow a critical assessment of numerical results.

Numerical Methods and Optimization – A Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied math

ematics.