Author | Hรคmmerlin, Gรผnther. author |
---|---|
Title | Numerical Mathematics [electronic resource] / by Gรผnther Hรคmmerlin, Karl-Heinz Hoffman |
Imprint | New York, NY : Springer New York, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4442-4 |
Descript | XII, 425 p. online resource |
1 Computing -- ยง1. Numbers and Their Representation -- ยง2. Floating Point Arithmetic -- ยง3. Error Analysis -- ยง4. Algorithms -- 2. Linear Systems of Equations -- ยง1. Gauss Elimination -- ยง2. The Cholesky Decomposition -- ยง3. The QR Decomposition of Householder -- ยง4. Vector Norms and Norms of Matrices -- ยง5. Error Bounds -- ยง6. III-Conditioned Problems -- 3. Eigenvalues -- ยง1. Reduction to Tridiagonal or Hessenberg Form -- ยง2. The Jacobi Rotation and Eigenvalue Estimates -- ยง3. The Power Method -- ยง4. The QR Algorithm -- 4. Approximation -- ยง1. Preliminaries -- ยง2. The Approximation Theorems of Weierstrass -- ยง3. The General Approximation Problem -- ยง4. Uniform Approximation -- ยง5. Approximation in Pre-Hilbert Spaces -- ยง6. The Method of Least Squares -- 5. Interpolation -- ยง1. The Interpolation Problem -- ยง2. Interpolation Methods and Remainders -- ยง3. Equidistant Interpolation Points -- ยง4. Convergence of Interpolating Polynomials -- ยง5. More on Interpolation -- ยง6. Multidimensional Interpolation -- 6. Splines -- ยง1. Polynomial Splines -- ยง2. Interpolating Splines -- ยง3. B-splines -- ยง4. Computing Interpolating Splines -- ยง5. Error Bounds and Spline Approximation -- ยง6. Multidimensional Splines -- 7. Integration -- ยง1. Interpolatory Quadrature -- ยง2. Extrapolation -- ยง3. Gauss Quadrature -- ยง4. Special Quadrature Methods -- ยง5. Optimality and Convergence -- ยง6. Multidimensional Integration -- 8. Iteration -- ยง1. The General Iteration Method -- ยง2. Newtonโs Method -- ยง3. Iterative Solution of Linear Systems of Equations -- ยง4. More on Convergence -- 9. Linear. Optimization -- ยง1. Introductory Examples and the General Problem -- ยง2. Polyhedra -- ยง3. The Simplex Method -- ยง4. Complexity Analysis -- References -- Symbols