Sylvester Equations (Not in Base Package)

Solves the Sylvester matrix equation. You can use this polymorphic VI to solve the Sylvester matrix equation for real matrixes or complex matrixes. The data types you wire to the A, B, and C inputs determine the polymorphic instance to use. Details  

Real Sylvester Equations

	operation A specifies the operation the VI performs on matrix A in the Sylvester equation. 0 not transposed (default)—op(A) = A 1 transposed—op(A) = transpose of A
	A contains matrix A in the Sylvester equation. A must be upper-triangular or upper quasi-triangular in canonical Schur form.
	B contains matrix B in the Sylvester equation. B must be upper-triangular or upper quasi-triangular in canonical Schur form.
	C contains matrix C in the Sylvester equation.
	sign specifies the form of the Sylvester equation. 0 plus (default)—op(A)X + Xop(B) = aC 1 minus—op(A)X – Xop(B) = aC
	operation B specifies the operation the VI performs on matrix B in the Sylvester equation. 0 not transposed (default)—op(B) = B 1 transposed—op(B) = transpose of B
	X returns the solution of the Sylvester equation.
	scale returns the scaling factor a of the Sylvester equation.
	perturbed indicates whether perturbed values are used to solve the equation. When perturbed is TRUE, the eigenvalues of A and B are common or close and indicates the solution of the Sylvester equation is not unique.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Complex Sylvester Equations

	operation A specifies the operation the VI performs on matrix A in the Sylvester equation. 0 not transposed (default)—op(A) = A 1 transposed—op(A) = conjugate transpose of A
	A contains matrix A in the Sylvester equation. A must be upper-triangular or upper quasi-triangular in canonical Schur form.
	B contains matrix B in the Sylvester equation. B must be upper-triangular or upper quasi-triangular in canonical Schur form.
	C contains matrix C in the Sylvester equation.
	sign specifies the form of the Sylvester equation. 0 plus (default)—op(A)X + Xop(B) = aC 1 minus—op(A)X – Xop(B) = aC
	operation B specifies the operation the VI performs on matrix B in the Sylvester equation. 0 not transposed (default)—op(B) = B 1 transposed—op(B) = conjugate transpose of B
	X returns the solution of the Sylvester equation.
	scale returns the scaling factor a of the Sylvester equation.
	perturbed indicates whether perturbed values are used to solve the equation. When perturbed is TRUE, the eigenvalues of A and B are common or close and indicates the solution of the Sylvester equation is not unique.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Sylvester Equations Details

The following equations define the Sylvester matrix equation.

op(A)X + Xop(B) = aC

or

op(A)X – Xop(B) = aC

where op(A) is A or the conjugate transpose of A, op(B) is B or the conjugate transpose of B, and a is a scaling factor used to avoid overflow in X.