This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the simplest linear iterative scheme one can think of, that is the successive iteration method (SI) x 0 ; x k+1 = Ax k + b; k 0 where A is a real or complex matrix of order n and x is a real or complex vector of size n. In exact arithmetic, the behaviour of (1) is completely understood ; there is convergenc...

The blockchain and cryptoasset sector, since coming to the attention of mainstream business financial markets during bitcoin bull run 2017, continues accelerate evolve rapidly. Decentralized finance (DeFi), a new iteration what was previously referred as open finance, has emerged an innovative use case service enabled by technology. As with any innovation or tool, however, there remains range q...

In this paper we rst review the construction of stable Riesz bases for nite element spaces with respect to Sobolev norms. Then, we construct optimal order multilevel preconditioners for the matrices in the normal form of the equations arising in the nite element discretization of non{symmetric second order elliptic equations. The optimality of the AMLI methods is proven under H 2 {regularity as...

This paper de nes and develops cycle indices for the nite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include semisimplicity, regularity, regular semisimplicity, the characteristic polynomial, number of Jordan blocks, and average order of a matrix.

A new approach of constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed The linear system arising from the mixed methods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which corresponds to a linear system generated by standard nonco...

Every in nite binary sequence is Turing reducible to a random one. This is a corollary of a result of P eter G acs stating that for every co-r.e. closed set with positive measure of in nite sequences there exists a computable mapping which maps a subset of the set onto the whole space of in nite sequences. Cristian Calude asked whether in this result one can replace the positive measure conditi...

A theory representing the dynamics of in nite population Genetic Algorithms is given by using Eigen's evolution model. The effect of crossover is included to study the evolution of in nite population GAs. We present a theory of GA dynamics, in which we give discrete time equations for GA evolution including the mutation and crossover processes. The Walsh analysis of allele frequencies provides ...

Bordered almost block diagonal systems arise from discretizing a linearized rst-order system of n ordinary diierential equations in a two-point boundary value problem with non-separated boundary conditions. The discretization may use spline collocation, nite diierences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standa...

where the matrix a(y)= (aij(y)) is symmetric positive de nite, whose entries are periodic functions of y with periodic cell Y . More speci cally we assume aij ∈C1; ( ); ¿ 0. It is also assumed that there exists positive constants a and a such that a‖ ‖2 6 aij(y) i j 6 a‖ ‖2 for all ∈ 2 and y∈ Y . The major goal in this paper is to develop a numerical approximation scheme on a mesh size h¿ (or h...