For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

We discuss irreducible polynomials that can be used to speed up square root extraction in fields of characteristic two. The obvious applications are to point halving methods for elliptic curves and divisor halving methods for hyperelliptic curves. Irreducible polynomials P (X) such that the square root ζ of a zero x of P (X) is a sparse polynomial are considered and those for which ζ has minima...

Moving the torso laterally in a walking biped robot can be mechanically more torque-e±cient than not moving the torso according to recent research. Motivated by this observation, a torque-e±cient torso-moving balance control strategy of a walking biped robot subject to a persistent continuous external force is suggested and veri ̄ed in this paper. The torso-moving balance control strategy consis...

Let A k ; k 0, be a sequence of m m nonnegative matrices and let A(z) = P 1 k=0 A k z k be such that A(1) is an irreducible stochastic matrix. The unique power-bounded solution of the nonlinear matrix equation G = P 1 k=0 A k G k has been shown to play a key role in the analysis of Markov chains of M/G/1 type. Assuming that the matrix A(z) is rational, we show that the solution of this matrix e...

We propose a primal-dual path-following Mehrotra-type predictor-corrector method for solving convex quadratic semidefinite programming (QSDP) problems. For the special case when the quadratic term has the form 1 2 X •(UXU), we compute the search direction at each iteration from the Schur complement equation. We are able to solve the Schur complement equation efficiently via the preconditioned s...

The purpose of this paper is to inquire the connection between maximal inner interval estimates of the solution sets to interval linear system and solutions of the dualization equation in Kaucher interval arithmetic. The results of our work are as follows: 1) a criterion of inner interval estimate of the solution set, 2) a criterion for a solution of dualization equation to be a maximal inner i...

Abstract We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution unilateral matrix equation associated with an M/G/1-type Markov chain. These derive from certain staircase regular splittings block Hessenberg M-matrix By exploiting profile, we introduce a two-step iteration. The iteration can be further by weighted average between approximat...