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Collected Problems in Numerical Methods
 Date: 21 April 2011, 11:02 Free register and download UseNet downloader, then you can FREE Download from UseNet.     Download without Limit " Collected Problems in Numerical Methods " from UseNet for FREE! CONTENTS Chapter 1 The approximate solution of non-linear algebraic and transcendental equations 1 1. Iterative methods for algebraic and transcendental equations of a single variable 2 Theory 1. Newton's method 2 2. The method of false position 2 3. Dandelin's method 3 4. The direct method of iteration 3 5. Bairstow's (or Hitchcock's) method for quadratic factors . . 3 6. Graeffe root squaring (or Lobachevskiy's) method 4 Problems 1-288 5 2. The solution of systems of non-linear equations 15 Theory 7. Newton's method for two simultaneous equations 15 8. An iteration method for systems of equations 16 Problems 289-301 16 References ' 18 Chapter 2 Numerical methods in linear algebra 19 1. The solution of systems of linear equations 20 Theory Exact methods 1. Gaussian elimination with complete pivoting 21 2. Compact Gaussian elimation without pivoting 22 3. The square-root or Cholesky's method 23 4. The method of orthogonalisation 24^LVI CONTENTS Iteratiye methods 5. A simple iterative method . 25 6. The Gauss-Seidel method 25 Methods for the inversion of matrices 7. The reinforcement method 26 8. An iterative method 26 9. Inversion by partitioning 26 Problems 1-69 27 2. The calculation of eigenvalues and eigenvectors of matrices ... 45 Theory Exact methods 10. Krylov's method 45 11. Danilevskiy's method 46 12. Faddeev's modification of Leverrier's method . .• 47 13. The interpolation method 48 Iteratiye methods 14. The classical method of Jacobi 48 15. Matrix powering 50 Problems 70-146 51 References 63 Chapter 3 Numerical solution of ordinary differential equations 65 1. First order differential equations 65 Theory 1. The Taylor series method 66 2. Euler's method 66 3. The modified Euler method 67 4. The modified Euler-Cauchy method 67 5. The modified Euler-Cauchy method with iteration 67 6. The Runge-Kutta method 68 7. Adam's method 68 8. The method of successive approximations 70 Problems 1-25 72 2, Systems of first order differential equations 77 Theory Problem 26 77^LCONTENTS VII 3. Second order differential equations 79 Theory 9. Reduction to first order systems 80 10. The Runge-Kutta method 80 11. Finite difference methods 80 Problem 27 81 ......

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