Condition number and backward errors of nonsymmetric algebraic Riccati equation

The normwise condition number and two kinds of backward errors are considered when nonsymmetric algebraic Riccati equation (NARE) has the minimal nonnegative solution. Based on the techniques for the symmetric case, we apply the condition number theory developed by Rice to define condition number for NARE. The explicit expression is derived in a uniform manner. Meanwhile, two kinds of backward errors are defined and evaluated by the explicit formulas. Numerical experiments are listed to illustrate and compare the practical performance.