The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms...

The main di culty in the implementation of most standard implicit Runge-Kutta (IRK) methods applied to (sti ) ordinary di erential equations (ODE's) is to e ciently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is ba...

(Rece;"cd 00 Monlh 20Ox; final ...,rsiaH recei"ed 00 Monlh £OOX) In this paper a primal-dual interior-point algorithm for semidefinite programming that can be used for analrzing e.g_ polytopic linear difleTential indusions is tailored in order to be more computationally efficient. The key to th" speedup is to allow for inexact ..,,,rch directions in the inteciOT_point algorithm. Th.,..., are ob...

Blind image deconvolution, a technique for obtaining restored as well the blur kernel from an inexact image. This research uses spatial characteristics to tackle problem of blind deconvolution. To work, proposed method does not necessitate prior information about kernel. Many applications, such remote sensing, astronomy, and medical X-ray imaging, deconvolution algorithms. study used maximum po...

The identification of instability in large-scale dynamical systems caused by Hopf bifurcation is difficult because of the problem of identifying the rightmost pair of complex eigenvalues of large sparse generalized eigenvalue problems. A new method developed in [Meerbergen and Spence, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 19821999] avoids this computation, instead performing an inverse ite...

In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is solved exactly. In his work we relax this requirement, and allow for the subp...

We consider a generalized Stokes equation with problem parameters 0 (size of the reaction term) and >0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess–Sarazin and Vanka-type smooth...

An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete network models from observations of multiple contin...