Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation

Iterative Solution of a Nonsymmetric Algebraic Riccati Equation

We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M -matrix or an irreducible singular M -matrix M . The solution of practical interest is the minimal nonnegative solution. We show that Newton’s method with zero initial guess can be used to find this solution without any further assumptions. We also present a qualitative perturb...

Differential Equation of Sensitivity Matrix for Final Velocity Constraint

Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory

We consider the solution of the large-scale nonsymmetric algebraic Riccati equation XCX À XD À AX þ B ¼ 0 from transport theory (Juang 1995), with M ½D; ÀC; ÀB; AŠ 2 R 2nÂ2n being a nonsingular M-matrix. In addition, A; D are rank-1 updates of diagonal matrices , with the products A À1 u; A À> u; D À1 v and D À> v computable in OðnÞ complexity, for some vectors u and v, and B, C are rank 1. The...

Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation

For the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix, the solution of practical interest is often the minimal nonnegative solution. In this note we prove that the minimal nonnegative solution is positive when the M -matrix is irreducible.