Contribution à la résolution numérique des équations de Laplace et de la chaleur
Convergence analysis of an inexact truncated RQ-iteration.
Convergence analysis of preconditioned AOR iterative method for linear systems.
Convergence and Comparison Analysis of Some Numerical Schwarz Methods.
Convergence of approximate splines via pseudo-inverses
Convergence of approximation methods for eigenvalue problem for two forms
The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space . We investigate some approximation methods generated by sequences of forms and defined on a dense subspace of . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.
Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations.
Convergence of infinite products of matrices and inner-outer iteration schemes.
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.
Convergence of nested classical iterative methods for linear systems.
Convergence of Rump's method for computing the Moore-Penrose inverse
We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the...
Convergence of the accelerated overrelaxation method
The convergence of the Accelerated Overrelaxation (AOR) method is discussed. It is shown that the intervals of convergence for the parameters and are not always of the following form: .
Convergence of the shifted QR algorithm on 3 x 3 normal matrices.
Convergence properties of ART and SOR algorithms.
Convergence rate estimate for a domain decomposition method.
Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem.
Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
We extend the analysis of the recently proposed nonlinear EIS scheme applied to the partial eigenvalue problem. We address the case where the Rayleigh quotient iteration is used as the smoother on the fine-level. Unlike in our previous theoretical results, where the smoother given by the linear inverse power method is assumed, we prove nonlinear speed-up when the approximation becomes close to the exact solution. The speed-up is cubic. Unlike existent convergence estimates for the Rayleigh quotient...
Convergence Theory of Extrapolated Iterative Methods for a Certain Class of Non-Symmetric Linear Systems.
Convergent Nonnegative Matrices and Iterative Methods for Consistent Linear Systems.
Counting determinants of Fibonacci-Hessenberg matrices using LU factorizations.