Algorithms For Several Matrix Equations

Matrix equations often arise in areas of scientific and engineering computing It is of great practical value to study this subject.In this thesis, an extended Sylvester conjugate matrix equation, a nonsym-metric algebraic Riccati equation from transport theory and the principle squareroot of a matrix are studied. The paper’s emphasis is on the discussion aboutthe nonsymmetric algebraic Riccati equation from transport theory.For an extended Sylvester conjugate matrix equation and a more generalcomplex matrix equation, an iterative algorithm based on the real representationof a complex matrix is proposed Complex operations aren’t involved in the newalgorithm.For the structure preserving doubling algorithm of a nonsymmetric algebraicRiccati equation from transport theory, a balancing strategy is proposed to reducethe cost of the computation. We demonstrate the efectiveness of the strategywith numerical tests and present the theoretical analysis.By employing the Cayley transformation and choosing an appropriate star-ing matrix, we devise a structure preserving doubling algorithm for the compu-tation of matrix principal square root.