in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Last time, we investigated the fourth-order Runge-Kutta method. We saw that the computations involved in performing this approximation were less than ideal. To create more computationally viable methods, we introduced multistep methods, in which the approximation at a given point is obtained using only the values of the differential equation to be approximated and the approximation itself at pr...

In this work we demonstrate two potential dangers of multiple-time-step techniques for numerical integration of differential equations. This idea of using different time steps for different interactions was proposed in 1978 for molecular dynamics but undoubtedly has other useful applications. The use of multiple time stepping with the popular Verlet method was proposed in a 1991 paper. However,...

The construction of s-stage explicit parallel two-step peer methods for the solution of non-stiff initial value problems with optimal zero stability and order p = s is considered. By an additional condition superconvergence of order p = s + 1 can be achieved. Further criteria for good methods are large stability regions and small error constants. Corresponding parameter sets have been obtained ...

‎‎‎in this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear volterra integral equations (2d-nvies) of the first kind‎. ‎here‎, ‎we convert a 2d-nvie of the first kind to a one-dimensional linear vie of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎we also verify convergence and error analysis of the method‎. ‎at t...

Some computable schemes for descent methods without line search are proposed. Convergence properties are presented. Numerical experiments concerning large scale unconstrained minimization problems are reported. Mathematical subject classification: 90C30, 65K05, 49M37.

A useful approach for long range computation of the Helmholtz equation in a waveguide is to re-formulate it as the operator diierential Riccati equation for the Dirichlet-to-Neumann (DtN) map. For waveguides with slow range dependence, the piecewise range independent approximation is used to derive a second order range stepping method for this one-way re-formulation. The range marching formulas...

In this paper we make an overview of s-step Conjugate Gradient and develop a novel formulation for s-step BiConjugate Gradient Stabilized iterative method. Also, we show how to add preconditioning to both of these s-step schemes. We explain their relationship to the standard, block and communication-avoiding counterparts. Finally, we explore their advantages, such as the availability of matrix-...

arcs in the set Z Of (1.1). These applications divide naturally into two classes. In the rst class, H models a parametrized physical system, which we wish to study as the parameter varies, such as in [12]. In the second class, we introduce an articial parameter in order to solve (or nd all solutions to) a system of n nonlinear equations in n unknowns for which locally convergent methods are ...

This paper describes a procedure to merge two STEP/AP EXPRESS schemata, using automated methods to assist the merging process. The desire to integrate or merge two schemata or ontologies is very common today (for example, it may be necessary to integrate two models describing car manufacturing from two different car manufacturing companies who just merged and need a common car manufacturing mod...