In this preliminary work, left and right conjugate vectors are deened for nonsymmetric, nonsin-gular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving nonsymmetric systems of linear equations is proposed. The method reduces to the usual conjugate gradient method when A is symmetric positive deenite. A nite termination property of th...

A continuous function f = u + iv is a complex valued harmonic function in a complex domain C if both u and v are real harmonic in C. In any simply connected domain D ⊂ C we can write f(z) = h + g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h′(...

In the eld of computational electrodynamics the discretization of Maxwell's equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extend...

Introduction.

We study random generation in the symmetric group when cycle type restrictions are imposed. Given $\pi, \pi' \in S_n$, we prove that $\pi$ and a conjugate of $\pi'$ likely to generate at least $A_n$ provided only have not too many fixed points $2$-cycles. As an application, investigate following question: For which positive integers $m$ should expect two elements order $A_n$? Among other things...

In this paper, a three-dimensional subspace method is proposed, in which the search direction generated by minimizing approximation model of objective function subspace. The not unique, and alternatives can be chosen between symmetric quadratic conic specific criteria. Moreover, idea WLY conjugate gradient applied to characterize change adjacent iteration points. strategy initial stepsize nonmo...

accurate calculation of reliability index is very important for the reliability analysis of structures. in some limit state functions with nonlinear characteristic and several local optimum design points, the computational reliability methods may not appropriately determine the failure probability, and iterative reliability approaches may be converged to local optimum design points. in this pap...