It is known that the solution of the semilinear matrix equation \(X - A\overline X B = C\) can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. We propose a method for solving the original semilinear equation in the normal case that permits to almost halve the execution time for equations of order n = 3000 compared to the library function dlyap, which solves Stein equations in Matlab.

中文翻译：

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正常情况下离散BHH方程的数值解

众所周知，可以简化半线性矩阵方程\（X-A \ overline XB = C \）的解，以求解经典的Stein方程。正常情况是指所得方程左侧的系数是正常矩阵。我们提出了一种在正常情况下求解原始半线性方程的方法，与库函数dlyap相比，该方法几乎可以将n = 3000阶方程的执行时间减少一半，后者可以在Matlab中求解Stein方程。