Circulant preconditioners for convolution-like integral equations with higher-order quadrature rules.
Combining the preconditioned conjugate gradient method and a matrix iterative method
The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.
Comparing multilevel coarsening strategies.
Concerning decomposition of a system of linear algebraic equations
Condition numbers of the Krylov bases and spaces associated with the truncated iteration.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Crout versions of ILU factorization with pivoting for sparse symmetric matrices.