Author | Jacques, Ian, 1957-. author |
---|---|
Title | Numerical Analysis [electronic resource] / by Ian Jacques, Colin Judd |
Imprint | Dordrecht : Springer Netherlands, 1987 |
Connect to | http://dx.doi.org/10.1007/978-94-009-3157-2 |
Descript | VIII, 326 p. online resource |
1 Introduction -- 1.1 Rounding errors and instability -- 2 Linear algebraic equations -- 2.1 Gauss elimination -- 2.2 Matrix decomposition methods -- 2.3 Iterative methods -- 3 Non-linear algebraic equations -- 3:1 Bracketing methods -- 3.2 Fixed point iteration -- 3.3 Newtonโs method -- 3.4 Systems of non-linear equations -- 4 Eigenvalues and eigenvectors -- 4.1 The power method -- 4.2 Deflation -- 4.3 Jacobiโs method -- 4.4 Sturm sequence iteration -- 4.5 Givensโ and Householderโs methods -- 4.6 The LR and QR methods -- 4.7 Hessenberg form -- 5 Methods of approximation theory -- 5.1 Polynomial interpolation: Lagrange form -- 5.2 Polynomial interpolation: divided difference form -- 5.3 Polynomial interpolation: finite difference form -- 5.4 Hermite interpolation -- 5.5 Cubic spline interpolation -- 5.6 Least squares approximation to discrete data -- 5.7 Least squares approximation to continuous functions -- 6 Numerical differentiation and integration -- 6.1 Numerical differentiation -- 6.2 Numerical integration: NewtonโCotes formulas -- 6.3 Quadrature rules in composite form -- 6.4 Rombergโs method -- 6.5 Simpsonโs adaptive quadrature -- 6.6 Gaussian quadrature -- 7 Ordinary differential equations: initial value problems -- 7.1 Derivation of linear multistep methods -- 7.2 Analysis of linear multistep methods -- 7.3 Runge-Kutta methods -- 7.4 Systems and higher order equations -- 8 Ordinary differential equations: boundary value problems -- 8.1 The finite difference method -- 8.2 The shooting method -- References -- Solutions to exercises