On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems
A framework and an algorithm for using modified Gram-Schmidt for constrained and weighted linear least squares problems is presented. It is shown that a direct implementation of a weighted modified Gram-Schmidt algorithm is unstable for heavily ...
Exact SOR convergence regions for a general class ofp-cyclic matrices
Linear systems whose associated block Jacobi iteration matrixB is weakly cyclic generated by the cyclic permutation σ = (σ1,σ2,..., σ p ) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding blockp-cyclic SOR ...
Stable approximation of fractional derivatives of rough functions
The process of numerical fractional differentiation is well known to be an ill-posed problem, and it has been discussed by many authors, and a large number of different solution methods has been proposed. However, available approaches require a ...
Stability analysis of numerical methods for systems of neutral delay-differential equations
Stability analysis of some representative numerical methods for systems of neutral delay-differential equations (NDDEs) is considered. After the establishment of a sufficient condition of asymptotic stability for linear NDDEs, the stability ...
A block incomplete orthogonalization method for large nonsymmetric eigenproblems
The incomplete orthogonalization method (IOM) proposed by Saad for computing a few eigenpairs of large nonsymmetric matrices is generalized into a block incomplete orthogonalization method (BIOM). It is studied how the departure from symmetry ‖A − ...
On a new kind of Birkhoff type trigonometric interpolation
In this paper we introduce a new kind of Birkhoff type interpolation of functions with period 2π. We find necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the ...
Time-marching algorithms for initial-boundary value problems based upon “approximate approximations”
New time marching algorithms for solving initial-boundary value problems for semi-linear parabolic and hyperbolic equations are described. With respect to the space variable the discretization is based upon a method of “ approximate approximation” ...
An interval iteration for multiple roots of transcendental equations
An iteration method for roots of algebraic functions with roots of multiplicity greater than one is established using tools and techniques from interval arithmetic. The method is based on an interval iteration functions for multiple roots and it ...
Lie-Butcher theory for Runge-Kutta methods
Runge-Kutta methods are formulated via coordinate independent operations on manifolds. It is shown that there is an intimate connection between Lie series and Lie groups on one hand and Butcher's celebrated theory of order conditions on the other. ...
Solution of sparse rectangular systems using LSQR and CRAIG
We examine two iterative methods for solving rectangular systems of linear equations: LSQR for over-determined systemsAx ≈ b, and Craig's method for under-determined systemsAx = b. By including regularization, we extend Craig's method to ...
On the bounds of approximations of holomorphic semigroups
The upper bounds of variable stepsize approximations of holomorphic semigroups are derived.
Heuristic investigation of chaotic mapping producing fractal objects
In the literature most examples on fractals are related to images produced by certain iterative processes. Here we will instead discuss how similar results may appear by mapping the unit circle using different, somewhat unusual functions. In ...
