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008    140509t20142014flua          001 0 eng d 
019 1  52764071 
020    9781466577770|q(cloth) 
039    CAVAL 
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050  4 QA297 
082 04 518|223 
100 1  Butenko, Sergiy,|eauthor. 
245 10 Numerical methods and optimization :|ban introduction /
       |cSergiy Butenko, Panos M. Pardalos. 
264  1 Boca Raton, FL :|bCRC Press,|c[2014] 
264  4 |c©2014 
300    xvi, 397 pages :|billustrations ;|c24 cm. 
336    text|btxt|2rdacontent 
337    unmediated|bn|2rdamedia 
338    volume|bnc|2rdacarrier 
490 1  Chapman & Hall/CRC numerical analysis and scientific 
       computing 
505 0  I.Basics -- 1.Preliminaries -- 1.1.Sets and Functions -- 
       1.2.Fundamental Theorem of Algebra -- 1.3.Vectors and 
       Linear (Vector) Spaces -- 1.3.1.Vector norms -- 
       1.4.Matrices and Their Properties -- 1.4.1.Matrix addition
       and scalar multiplication -- 1.4.2.Matrix multiplication -
       - 1.4.3.The transpose of a matrix -- 1.4.4.Triangular and 
       diagonal matrices -- 1.4.5.Determinants -- 1.4.6.Trace of 
       a matrix -- 1.4.7.Rank of a matrix -- 1.4.8.The inverse of
       a nonsingular matrix -- 1.4.9.Eigenvalues and eigenvectors
       -- 1.4.10.Quadratic forms -- 1.4.11.Matrix norms -- 
       1.5.Preliminaries from Real and Functional Analysis -- 
       1.5.1.Closed and open sets -- 1.5.2.Sequences -- 
       1.5.3.Continuity and differentiability -- 1.5.4.Big O and 
       little o notations -- 1.5.5.Taylor's theorem -- 2.Numbers 
       and Errors -- 2.1.Conversion between Different Number 
       Systems -- 2.1.1.Conversion of integers -- 
       2.1.2.Conversion of fractions -- 2.2.Floating Point 
       Representation of Numbers -- 
505 0  Contents note continued: 2.3.Definitions of Errors -- 
       2.4.Round-off Errors -- 2.4.1.Rounding and chopping -- 
       2.4.2.Arithmetic operations -- 2.4.3.Subtractive 
       cancellation and error propagation -- II.Numerical Methods
       for Standard Problems -- 3.Elements of Numerical Linear 
       Algebra -- 3.1.Direct Methods for Solving Systems of 
       Linear Equations -- 3.1.1.Solution of triangular systems 
       of linear equations -- 3.1.2.Gaussian elimination -- 
       3.1.2.1.Pivoting strategies -- 3.1.3.Gauss-Jordan method 
       and matrix inversion -- 3.1.4.Triangular factorization -- 
       3.2.Iterative Methods for Solving Systems of Linear 
       Equations -- 3.2.1.Jacobi method -- 3.2.2.Gauss-Seidel 
       method -- 3.2.3.Application: input-output models in 
       economics -- 3.3.Overdetermined Systems and Least Squares 
       Solution -- 3.3.1.Application: linear regression -- 
       3.4.Stability of a Problem -- 3.5.Computing Eigenvalues 
       and Eigenvectors -- 3.5.1.The power method -- 
       3.5.2.Application: ranking methods -- 4.Solving Equations 
       -- 
505 0  Contents note continued: 4.1.Fixed Point Method -- 
       4.2.Bracketing Methods -- 4.2.1.Bisection method -- 
       4.2.1.1.Convergence of the bisection method -- 
       4.2.1.2.Intervals with multiple roots -- 4.2.2.Regula-
       falsi method -- 4.2.3.Modified regula-falsi method -- 
       4.3.Newton's Method -- 4.3.1.Convergence rate of Newton's 
       method -- 4.4.Secant Method -- 4.5.Solution of Nonlinear 
       Systems -- 4.5.1.Fixed point method for systems -- 
       4.5.2.Newton's method for systems -- 5.Polynomial 
       Interpolation -- 5.1.Forms of Polynomials -- 
       5.2.Polynomial Interpolation Methods -- 5.2.1.Lagrange 
       method -- 5.2.2.The method of undetermined coefficients --
       5.2.3.Newton's method -- 5.3.Theoretical Error of 
       Interpolation and Chebyshev Polynomials -- 
       5.3.1.Properties of Chebyshev polynomials -- 6.Numerical 
       Integration -- 6.1.Trapezoidal Rule -- 6.2.Simpson's Rule 
       -- 6.3.Precision and Error of Approximation -- 
       6.4.Composite Rules -- 6.4.1.The composite trapezoidal 
       rule -- 6.4.2.Composite Simpson's rule -- 
505 0  Contents note continued: 6.5.Using Integrals to 
       Approximate Sums -- 7.Numerical Solution of Differential 
       Equations -- 7.1.Solution of a Differential Equation -- 
       7.2.Taylor Series and Picard's Methods -- 7.3.Euler's 
       Method -- 7.3.1.Discretization errors -- 7.4.Runge-Kutta 
       Methods -- 7.4.1.Second-order Runge-Kutta methods -- 
       7.4.2.Fourth-order Runge-Kutta methods -- 7.5.Systems of 
       Differential Equations -- 7.6.Higher-Order Differential 
       Equations -- III.Introduction to Optimization -- 8.Basic 
       Concepts -- 8.1.Formulating an Optimization Problem -- 
       8.2.Mathematical Description -- 8.3.Local and Global 
       Optimality -- 8.4.Existence of an Optimal Solution -- 
       8.5.Level Sets and Gradients -- 8.6.Convex Sets, Functions,
       and Problems -- 8.6.1.First-order characterization of a 
       convex function -- 8.6.2.Second-order characterization of 
       a convex function -- 9.Complexity Issues -- 9.1.Algorithms
       and Complexity -- 9.2.Average Running Time -- 
       9.3.Randomized Algorithms -- 
505 0  Contents note continued: 9.4.Basics of Computational 
       Complexity Theory -- 9.4.1.Class NP -- 9.4.2.P vs. NP -- 
       9.4.3.Polynomial time reducibility -- 9.4.4.NP-complete 
       and NP-hard problems -- 9.5.Complexity of Local 
       Optimization -- 9.6.Optimal Methods for Nonlinear 
       Optimization -- 9.6.1.Classes of methods -- 
       9.6.2.Establishing lower complexity bounds for a class of 
       methods -- 9.6.3.Defining an optimal method -- 
       10.Introduction to Linear Programming -- 10.1.Formulating 
       a Linear Programming Model -- 10.1.1.Defining the decision
       variables -- 10.1.2.Formulating the objective function -- 
       10.1.3.Specifying the constraints -- 10.1.4.The complete 
       linear programming formulation -- 10.2.Examples of LP 
       Models -- 10.2.1.A diet problem -- 10.2.2.A resource 
       allocation problem -- 10.2.3.A scheduling problem -- 
       10.2.4.A mixing problem -- 10.2.5.A transportation problem
       -- 10.2.6.A production planning problem -- 10.3.Practical 
       Implications of Using LP Models -- 
505 0  Contents note continued: 10.4.Solving Two-Variable LPs 
       Graphically -- 10.5.Classification of LPs -- 11.The 
       Simplex Method for Linear Programming -- 11.1.The Standard
       Form of LP -- 11.2.The Simplex Method -- 11.2.1.Step 1 -- 
       11.2.2.Step 2 -- 11.2.3.Recognizing optimality -- 
       11.2.4.Recognizing unbounded LPs -- 11.2.5.Degeneracy and 
       cycling -- 11.2.6.Properties of LP dictionaries and the 
       simplex method -- 11.3.Geometry of the Simplex Method -- 
       11.4.The Simplex Method for a General LP -- 11.4.1.The two
       -phase simplex method -- 11.4.2.The big-M method -- 
       11.5.The Fundamental Theorem of LP -- 11.6.The Revised 
       Simplex Method -- 11.7.Complexity of the Simplex Method --
       12.Duality and Sensitivity Analysis in Linear Programming 
       -- 12.1.Defining the Dual LP -- 12.1.1.Forming the dual of
       a general LP -- 12.2.Weak Duality and the Duality Theorem 
       -- 12.3.Extracting an Optimal Solution of the Dual LP from
       an Optimal Tableau of the Primal LP -- 
505 0  Contents note continued: 12.4.Correspondence between the 
       Primal and Dual LP Types -- 12.5.Complementary Slackness -
       - 12.6.Economic Interpretation of the Dual LP -- 
       12.7.Sensitivity Analysis -- 12.7.1.Changing the objective
       function coefficient of a basic variable -- 
       12.7.2.Changing the objective function coefficient of a 
       nonbasic variable -- 12.7.3.Changing the column of a 
       nonbasic variable -- 12.7.4.Changing the right-hand side -
       - 12.7.5.Introducing a new variable -- 12.7.6.Introducing 
       a new constraint -- 12.7.7.Summary -- 13.Unconstrained 
       Optimization -- 13.1.Optimality Conditions -- 13.1.1.First
       -order necessary conditions -- 13.1.2.Second-order 
       optimality conditions -- 13.1.3.Using optimality 
       conditions for solving optimization problems -- 
       13.2.Optimization Problems with a Single Variable -- 
       13.2.1.Golden section search -- 13.2.1.1.Fibonacci search 
       -- 13.3.Algorithmic Strategies for Unconstrained 
       Optimization -- 13.4.Method of Steepest Descent -- 
505 0  Contents note continued: 13.4.1.Convex quadratic case -- 
       13.4.2.Global convergence of the steepest descent method -
       - 13.5.Newton's Method -- 13.5.1.Rate of convergence -- 
       13.5.2.Guaranteeing the descent -- 13.5.3.Levenberg-
       Marquardt method -- 13.6.Conjugate Direction Method -- 
       13.6.1.Conjugate direction method for convex quadratic 
       problems -- 13.6.2.Conjugate gradient algorithm -- 
       13.6.2.1.Non-quadratic problems -- 13.7.Quasi-Newton 
       Methods -- 13.7.1.Rank-one correction formula -- 
       13.7.2.Other correction formulas -- 13.8.Inexact Line 
       Search -- 14.Constrained Optimization -- 14.1.Optimality 
       Conditions -- 14.1.1.First-order necessary conditions -- 
       14.1.1.1.Problems with equality constraints -- 
       14.1.1.2.Problems with inequality constraints -- 
       14.1.2.Second-order conditions -- 14.1.2.1.Problems with 
       equality constraints -- 14.1.2.2.Problems with inequality 
       constraints -- 14.2.Duality -- 14.3.Projected Gradient 
       Methods -- 14.3.1.Affine scaling method for LP -- 
       14.4.Sequential Unconstrained Minimization -- 
       14.4.1.Penalty function methods -- 14.4.2.Barrier methods 
       -- 14.4.3.Interior point methods. 
650  0 Numerical analysis.  
650  0 Numerical functions. 
650  0 Functional analysis. 
650  0 Mathematical optimization. 
700 1  Pardalos, Panow M.,|eauthor. 
830  0 Chapman & Hall/CRC numerical analysis and scientific 
       computing. 
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