The Barzilai-Borwein method, an effective gradient descent method with cleaver choice of the step-length, is adapted from nonlinear optimization to Riemannian manifold optimization. More generally, global convergence of a nonmonotone line-search strategy for Riemannian optimization algorithms is proved under some standard assumptions. By a set of numerical tests, the Riemannian Barzilai-Borwein...

 Transient simulation times for field-circuit coupled models of realistic electromagnetic devices become unacceptably high. A magnetodynamic formulation is coupled to an electric circuit analysis, yielding a sparse, symmetric and indefinite matrix. The unknown circuit currents correspond to negative eigenvalues in the matrix spectrum. The Quasi-Minimal Residual method performs better than the ...

In the case that the matrix of a linear complementarity problem consists of the sum of a positive semi-definite matrix and a co-positive matrix a general condition is deduced implying that the Lemke algorithm will terminate with a complementarity solution. Applications are presented on bi-matrix games, convex quadratic programming and multi-period programs.

In this paper we consider the positive definite solutions of nonlinear matrix equation X + A X−δA = Q, where δ ∈ (0, 1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632–645]. The necessary and sufficient conditions for the existence of a solution are derived. An it...

The asymptotic behavior of #n (d;) #n (d:) and Pn (x, d;) P n (x, d:) is studied. Here (#n (.))n are the leading coefficients of the orthonormal matrix polynomials Pn (x, .) with respect to the matrix measures d; and d: which are related by d;(u)= d:(u)+ k=1 Mk$(u&ck), where Mk are positive definite matrices, $ is the Dirac measure and ck lies outside the support of d: for k=1, ..., N. Finally,...

In this paper Kharitonov's t h e o m for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. It is shown that if the four Hemite matrices correspondii to the four Kharitonov extreme polynomials are positive definite, the Hermite...

The numerical solution of large-scale continuous-time Lyapunov matrix equations is of great importance in many application areas. Assuming that the coefficient matrix is positive definite, but not necessarily symmetric, in this paper we analyze the convergence of projection type methods for approximating the solution matrix. Under suitable hypotheses on the coefficient matrix, we provide new as...

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...

In this paper Kharitonov's theorem for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. I t is shown that if the four Hermite matrices corresponding to the four Kharitonov extreme polynomials are positive definite, the Hermit...