On Tuesday, September 9, 2014 4:33 PM, ling huang <ling.huang@p
On Tuesday, September 9, 2014 4:33 PM, ling huang <[email protected]> wrote: Thought this may be of interest for those using numerical optimization methods in ecology applications. Cheers Ling Ling Huang Sacramento City College http://huangl.webs.com On Tuesday, September 9, 2014 7:20 AM, Eric WALTER <[email protected]> wrote: New book: Numerical Methods and Optimization, A Consumer Guide by Eric Walter (Laboratoire des Signaux et Systèmes, CNRS, Supélec, Université Paris-Sud), Springer, Cham, 2014, 476 p., 67 illus., 23 illus. in color. Abstract: 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 (1) 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; (2) understand the principles behind recognized algorithms used in state-of-the-art numerical software; (3) 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 (4) acquire methods that allow a critical assessment of numerical results. For more information: http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-319-07670-6 Content: 1 From Calculus to Computation (Why Not Use Naive Mathematical Methods? What to Do, Then? How Is This Book Organized? References) 2 Notation and Norms (Scalars, Vectors, and Matrices, Derivatives, Little o and Big O, Norms, Reference) 3 Solving Systems of Linear Equations (Examples, Condition Number(s), Approaches Best Avoided, Questions About A, Direct Methods, Iterative Methods, Taking Advantage of the Structure of A, Complexity Issues, MATLAB Examples, In Summary, References) 4 Solving Other Problems in Linear Algebra (Inverting Matrices, Computing Determinants, Computing Eigenvalues and Eigenvectors, MATLAB Examples, In Summary, References) 5 Interpolating and Extrapolating (Examples, Univariate Case, Multivariate Case, MATLAB Examples, In Summary, References) 6 Integrating and Differentiating Functions (Examples, Integrating Univariate Functions, Integrating Multivariate Functions, Differentiating Univariate Functions, Differentiating Multivariate Functions, Automatic Differentiation, MATLAB Examples, In Summary, References) 7 Solving Systems of Nonlinear Equations (What Are the Differences with the Linear Case? Examples, One Equation in One Unknown, Multivariate Systems, Where to Start From? When to Stop? MATLAB Examples, In Summary, References) 8 Introduction to Optimization (A Word of Caution, Examples, Taxonomy, How About a Free Lunch? In Summary, References) 9 Optimizing Without Constraint (Theoretical Optimality Conditions, Linear Least Squares, Iterative Methods, Additional Topics, MATLAB Examples, In Summary, References) 10 Optimizing Under Constraints (Theoretical Optimality Conditions, Solving the KKT Equations with Newton’s Method, Using Penalty or Barrier Functions, Sequential Quadratic Programming, Linear Programming, Convex Optimization, Constrained Optimization on a Budget, MATLAB Examples, In Summary, References) 11 Combinatorial Optimization (Simulated Annealing, MATLAB Example, References) 12 Solving Ordinary Differential Equations (Initial-Value Problems, Boundary-Value Problems, MATLAB Examples, In Summary, References) 13 Solving Partial Differential Equations (Classification, Finite-Difference Method, A Few Words About the Finite-Element Method, MATLAB Example, In Summary, References) 14 Assessing Numerical Errors (Types of Numerical Algorithms, Rounding, Cumulative Effect of Rounding Errors, Classes of Methods for Assessing Numerical Errors, CESTAC/CADNA, MATLAB Examples, In Summary, References) 15 WEB Resources to Go Further (Search Engines, Encyclopedias, Repositories, Software, OpenCourseWare, References) 16 Problems (Ranking Web Pages, Designing a Cooking Recipe, Landing on the Moon, Characterizing Toxic Emissions by Paints, Maximizing the Income of a Scraggy Smuggler, Modeling the Growth of Trees, Detecting Defects in Hardwood Logs, Modeling Black-Box Nonlinear Systems, Designing a Predictive Controller, Discovering and Using Recursive Least Squares, Building a Lotka–Volterra Model, Modeling Signals by Prony’s Method, Maximizing Performance, Modeling AIDS Infection, Looking for Causes, Maximizing Chemical Production, Discovering the Response-Surface Methodology, Estimating Microparameters via Macroparameters, Solving Cauchy Problems for Linear ODEs, Estimating Parameters Under Constraints, Estimating Parameters with lp Norms, Dealing with an Ambiguous Compartmental Model, Inertial Navigation, Modeling a District Heating Network, Optimizing Drug Administration, Shooting at a Tank, Sparse Estimation Based on POCS, References) Index
