Introductory Material |
Vector and matrices norms |
Eigenvalues |
Irreducibility and diagonal dominance |
M--Matrices and generalizations |
Splittings |
Positive definite matrices |
The graph of a matrix |
Chebyshev polynomials |
Discretization methods for partial diffential equations |
Eigenvalues and Fourier analysis |
Floating point arithmetic |
Vector and parallel computers |
BLAS and LAPACK |
Bibliographical comments |
Gaussian elimination for general linear systems |
Introduction to Gaussian elimination |
Gaussian elimination without permutations |
Gaussian elimination with permutations (partial piv-oting) |
Gaussian elimination with other pivoting strategies |
Operation counts |
Gaussian elimination for symmetric systems |
The outer product algorithm |
The bordering algorithm |
The inner product algorithm |
Coding the three factorization algorithms |
Positive definite systems |
Indefinite systems |
Gaussian elimination for H-matrices |
Block methods |
Tridiagonal and block tridiagonal systems |
Roundoff error analysis |
Perturbation analysis |
Scaling |
Iterative refinement |
Parallel solution of general linear systems |
Gaussian elimination for sparse linear systems |
Introduction |
The fill--in phenomenon |
Graphs and fill--in for symmetric matrices |
Characterization of the fill--in |
Band and envelope numbering schemes for symmetric matrices |
The Cuthill--McKee and reverse Cuthill--McKee orderings |
Sloan's algorithm |
Spectral schemes |
The basic idea |
The multilevel spectral algorithm |
The Kumfert and Pothen hybrid algorithm |
The Boman--Hendrickson multilevel algorithm |
The minimum degree ordering |
The nested dissection ordering |
Generalization of dissection algorithms |
General dissection algorithms |
Graph bisection improvement techniques |
The multisection algorithm |
The multifrontal method |
Non--symmetric sparse matrices |
Numerical stability for sparse matrices |
Parallel algorithms for sparse matrices |
Fast solvers for separable PDEs |
Fast Fourier Transform |
The basics of the FFT |
The complex FFT |
The real transforms |
FFT on vector and parallel computers |
Stability of the FFT |
Other algorithms |
Double Fourier analysis |
The Fourier tridiagonal Method |
The cyclic reduction method |
The FACR(l) method |
The capacitance matrix method |
Classical iterative methods |
The Jacobi method |
The Gauss-Seidel method |
The SOR Method |
The SSOR method |
Alternating direction methods |
Richardson methods |
Acceleration techniques |
Stability of classical iterative methods |
The conjugate gradient and related methods |
Introductory Material |
Vector and matrices norms |
Eigenvalues |
Irreducibility and diagonal dominance |
M--Matrices and generalizations |
Splittings |