{"product_id":"numerical-methods-for-unconstrained-optimization-and-nonlinear-equations-paperback-softback-9780898713640","title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Paperback \/ softback) 9780898713640","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eNumerical Methods for Unconstrained Optimization and Nonlinear Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJ.e. Dennis Jr (Author), Robert B. Schnabel (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898713640, Society for Industrial and Applied Mathematics\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 31 December 1996\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e396 pages\u003cbr\u003e22.8 x 15.2 x 2.2 cm, 0.56 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or 'quasi-Newton' methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Introduction. Problems to be considered\u003cbr\u003e Characteristics of 'real-world' problems\u003cbr\u003e Finite-precision arithmetic and measurement of error\u003cbr\u003e Exercises\u003cbr\u003e 2. Nonlinear Problems in One Variable. What is not possible\u003cbr\u003e Newton's method for solving one equation in one unknown\u003cbr\u003e Convergence of sequences of real numbers\u003cbr\u003e Convergence of Newton's method\u003cbr\u003e Globally convergent methods for solving one equation in one uknown\u003cbr\u003e Methods when derivatives are unavailable\u003cbr\u003e Minimization of a function of one variable\u003cbr\u003e Exercises\u003cbr\u003e 3. Numerical Linear Algebra Background. Vector and matrix norms and orthogonality\u003cbr\u003e Solving systems of linear equations—matrix factorizations\u003cbr\u003e Errors in solving linear systems\u003cbr\u003e Updating matrix factorizations\u003cbr\u003e Eigenvalues and positive definiteness\u003cbr\u003e Linear least squares\u003cbr\u003e Exercises\u003cbr\u003e 4. Multivariable Calculus Background\u003cbr\u003e Derivatives and multivariable models\u003cbr\u003e Multivariable finite-difference derivatives\u003cbr\u003e Necessary and sufficient conditions for unconstrained minimization\u003cbr\u003e Exercises\u003cbr\u003e 5. Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton's method for systems of nonlinear equations\u003cbr\u003e Local convergence of Newton's method\u003cbr\u003e The Kantorovich and contractive mapping theorems\u003cbr\u003e Finite-difference derivative methods for systems of nonlinear equations\u003cbr\u003e Newton's method for unconstrained minimization\u003cbr\u003e Finite difference derivative methods for unconstrained minimization\u003cbr\u003e Exercises\u003cbr\u003e 6. Globally Convergent Modifications of Newton's Method. The quasi-Newton framework\u003cbr\u003e Descent directions\u003cbr\u003e Line searches\u003cbr\u003e The model-trust region approach\u003cbr\u003e Global methods for systems of nonlinear equations\u003cbr\u003e Exercises\u003cbr\u003e 7. Stopping, Scaling, and Testing. Scaling\u003cbr\u003e Stopping criteria\u003cbr\u003e Testing\u003cbr\u003e Exercises\u003cbr\u003e 8. Secant Methods for Systems of Nonlinear Equations. Broyden's method\u003cbr\u003e Local convergence analysis of Broyden's method\u003cbr\u003e Implementation of quasi-Newton algorithms using Broyden's update\u003cbr\u003e Other secant updates for nonlinear equations\u003cbr\u003e Exercises\u003cbr\u003e 9. Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell\u003cbr\u003e Symmetric positive definite secant updates\u003cbr\u003e Local convergence of positive definite secant methods\u003cbr\u003e Implementation of quasi-Newton algorithms using the positive definite secant update\u003cbr\u003e Another convergence result for the positive definite secant method\u003cbr\u003e Other secant updates for unconstrained minimization\u003cbr\u003e Exercises\u003cbr\u003e 10. Nonlinear Least Squares. The nonlinear least-squares problem\u003cbr\u003e Gauss-Newton-type methods\u003cbr\u003e Full Newton-type methods\u003cbr\u003e Other considerations in solving nonlinear least-squares problems\u003cbr\u003e Exercises\u003cbr\u003e 11. Methods for Problems with Special Structure. The sparse finite-difference Newton method\u003cbr\u003e Sparse secant methods\u003cbr\u003e Deriving least-change secant updates\u003cbr\u003e Analyzing least-change secant methods\u003cbr\u003e Exercises\u003cbr\u003e Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel)\u003cbr\u003e Appendix B. Test Problems (by Robert Schnabel)\u003cbr\u003e References\u003cbr\u003e Author Index\u003cbr\u003e Subject Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52502957162776,"sku":"9780898713640","price":51.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898713640i.jpg?v=1786321253","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/numerical-methods-for-unconstrained-optimization-and-nonlinear-equations-paperback-softback-9780898713640","provider":"Freshly Printed Books","version":"1.0","type":"link"}