Matrix.Sylvester Method

function Sylvester(A: TMtx; B: TMtx; C: TMtx; ASign: TSign; AOp: TMtxOperation; BOp: TMtxOperation): Double;

Solves the Sylvester equation.

#NameTypeDescription
1ATMtxsource TMtx
2BTMtxsource TMtx
3CTMtxsource TMtx
4ASignTSign
5AOpTMtxOperation
6BOpTMtxOperation

Returns: Double

Remarks:

Solves the Sylvester's equation

op(A)X±Xop(B)=αC\text{op}(A)\cdot X \pm X\cdot \text{op}(B) = \alpha C

for real quasi-triangular or complex triangular matrices A and B. The solution (X) overwrites the C matrix. The AOp and BOp parameters indicate the TMtxOperation performed on A and B respectively. The TSign of the Sylvester equation is determined with the ASign parameter (siPlus for +, siMinus for -). The result of a Sylvester function is a scale factor a. The A and B matrices Matrix.Quadratic property must be true, otherwise an exception is raised.