Conjugate points, triangular matrices, and Riccati equations

Conjugate points, triangular matrices, and Riccati equations

Let A be a real continuous nxn matrix on an interval T3 and let the n-vector x be a solution of the differential equation x = Ax on r. If [oc,g]er, g is called a conjugate point of a if the equation has a nontrivial solution vector x = (x1,...,xn) such that x1(a) = ... = xk(a) = x k+1(P) = ... = x (0) = 0 for some ke[l,n-l]. It is shown that the absence on (t..,t ) of a point conjugate to t, wi...

Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices

We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.

Perturbation theory for Hamiltonian operator matrices and Riccati equations

TRIANGULAR FUZZY MATRICES

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

On algebraic Riccati equations associated with M -matrices

We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M ...