An Integral-Interpolation Iterative Method for the Solution of Scalar Equations.
We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter which defines the size of the neighborhood of the central-path and of the parameter which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges...
This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.
Here is presented a 6-states non minimal-time solution which is intrinsically Minsky-like and solves the three following problems: unrestricted version on a line, with one initiator at each end of a line and the problem on a ring. We also give a complete proof of correctness of our solution, which was never done in a publication for Minsky's solutions.
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....
One parabolic integrodifferential problem in the abstract real Hilbert spaces is studied in this paper. The semidiscrete and full discrete approximate solution is defined and the error estimate of Rothe's function in some function spaces is established.