Numerical Methods and Optimization : A Consumer Guide

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. 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. Front Matter....Pages i-xv From Calculus to Computation....Pages 1-6 Notation and Norms....Pages 7-16 Solving Systems of Linear Equations....Pages 17-57 Solving Other Problems in Linear Algebra....Pages 59-76 Interpolating and Extrapolating....Pages 77-97 Integrating and Differentiating Functions....Pages 99-138 Solving Systems of Nonlinear Equations....Pages 139-165 Introduction to Optimization....Pages 167-175 Optimizing Without Constraint....Pages 177-244 Optimizing Under Constraints....Pages 245-288 Combinatorial Optimization....Pages 289-298 Solving Ordinary Differential Equations....Pages 299-358 Solving Partial Differential Equations....Pages 359-378 Assessing Numerical Errors....Pages 379-407 WEB Resources to Go Further....Pages 409-414 Problems....Pages 415-468 Back Matter....Pages 469-476