New method for square root of non-singular M-matrix

Square root of a matrix play an important role in many applications of matrix theory. In this paper, we propose a new iterative method for square root of a non-singular M-matrix. We first transform the matrix equation X2 – A=0 into special form of a non-symmetric algebraic Riccati equation (NARE), and then solve this special NARE by Newton method. Efficiency and effectiveness proved by theoretical analysis and numerical experiments. Keywords: - Matrix square root, M-matrix, Non-symmetric algebraic Riccati equation, Newton method

Efficient Numerical Algorithms for Balanced Stochastic Truncation

We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation of balanced stochastic truncation model reduction

A matrix equation arising in statistical filter theory

Solution of Ricatti differential equation arising in statistical filering and optimal control theor

Oving Eigenvalues and Eigenvectors

The Office of Naval Research Department Of The Navy Contract No. N 00014-67-A-0305-0010 ; Project No. NR 064-183/5-28-70(439

A model-trust region algorithm utilizing a quadratic interpolant

AbstractA new model-trust region algorithm for problems in unconstrained optimization and nonlinear equations utilizing a quadratic interpolant for step selection is presented and analyzed. This is offered as an alternative to the piecewise-linear interpolant employed in the widely used “double dogleg” step selection strategy. After the new step selection algorithm has been presented, we offer a summary, with proofs, of its desirable mathematical properties. Numerical results illustrating the efficacy of this new approach are presented

Methods of applied dynamics

The monograph was prepared to give the practicing engineer a clear understanding of dynamics with special consideration given to the dynamic analysis of aerospace systems. It is conceived to be both a desk-top reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject. Beginning with the basic concepts of kinematics and dynamics, the discussion proceeds to treat the dynamics of a system of particles. Both classical and modern formulations of the Lagrange equations, including constraints, are discussed and applied to the dynamic modeling of aerospace structures using the modal synthesis technique

Identification of Systems

Quasilinearization for system identification and programming strategie