Numerical analysis and scientific computation = 数值分析与科学计算 /

1 Nonlinear Equations 11.1 Bisechon and inverse Linear interpolation 1l.2 Newton's Method 1 11.3 The Feed Point Theorem ZIl.4 Quadratic Convenience or~ton's Mettiod 31I.5 vacants of Newton's Method 43I.6 Brent'SMethed 5517 Effects of Finite incision Anthmetic 62l.8 Newton's Method for Systems 73l.9 Broyden's Method 832 Linear Systems goZI Gaussian EI~on with Pallial Pivoting 902.2 The LUDecomposihon 1022.3 The LU boomposition with Pivohng 1132,4 ThectioIests Decomposition 12825 Condition Numbers 1402.6 The QRDecompositioD 1532.7 Householder Triangulanzation and theoR DecompDSition 1652,8 Gram SCh~ OWhogunanzation and theQRDecomnosihon 1772.9 The Singulax Value Decomposition 190vin Contents3 lterative Methods is63] Jarobi and Gauss-Seidel Jteration 1963.2 Sparslty 2083.3 Iterative Refinement 2143.4 Preconditiomng 21935 KryIOV Space Mithods 22636 NamcricaI EgennrobIems 2384 Polynomial Im6rpolation 24741 Lasrange JnterooIating POlynomialS z#742 Piccewl sc Linear intmpolatlon 26 14.3 Cubic SpInies 2744.4 COmmutation of the Cubic Spline COemcients 2845 Numerical Integration 2985.1 Closed Newton Cotes F'ormulas 2985.2 Open Newton-Cotes Formulas and UndetendnedCoefficients 3165.3 GaussianQuaurature 3305.4 tuuss Chetryshev Quactraturc 34255 Radau and LChami Quadrature 3515.6 Adaptivity and Automatic Integtation 3615.7 Ronlberglniegtation 3716 Differential Equations afl61 Numencal Differenhation 3816.2 EuIer's MCthod 3926.3 I]nproved EIIIer's Me~ 4026.4 Analysis offupIicit One Step Mithods 4II6.5 ThyIOr ac Runge-Kutta Methods 4196.6 Adantivity and Styness 42867 Mulh StePMethods 4377 Nonlinear Optimization 4467.1 O]le-Dunensional Searches 4467.2 The Method of Steepest Descent 455COntents IX7.3 Newton Methods for Nonlinear OPhndzation co77.4 Multiple Random Sac Methods 4777.5 DrmctSeedMethods 4857.6 The Nelder-Maal Method 4937.7 COnjugate Dbechon thetheds 5008 Approximation Methods sos8.1 Linear and Nonlinear ~t Squares 5058.2 The Best ^nproxunarmn Problem 51783 Best UnifOTrn Approximation 5258.4 APplications of the Chebyshev Polynomials 538Aff6rwoed 645Answers s49Bibliography s7iIndex s77