The quadratic matrix equation AX2 + B X +C = 0 in n ×n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration m...

quadratic equation is eigen-decomposed to build a linear This paper proposes a linear algorithm for metric equation to compute the projective-to-Euclidean trans-reconstruction from projective reconstruction. Metric formation matrix. reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We buil...

The problem of reducing an algebraic Riccati equation XCX −AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX + QX + R = 0 is analyzed. New reductions are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm of B.D.O. Anderson [Internat. J. Control, 1978] is in fact...

This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...

We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algor...

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n × n quadratic matrix equation X − L1X − L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear s...