Package jline.lib.SMC

Class QBD_NI_SylvestKt

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    • Method Summary

      Modifier and Type Method Description
      final static Matrix QBD_NI_Sylvest(Matrix A, Matrix B, Matrix C, Matrix D) Solves the Sylvester equation AXB + CX = D using complex Schur and Hessenberg-triangular decomposition.
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        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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    • Method Detail

      • QBD_NI_Sylvest

         final static Matrix QBD_NI_Sylvest(Matrix A, Matrix B, Matrix C, Matrix D)

        Solves the Sylvester equation AXB + CX = D using complex Schur and Hessenberg-triangular decomposition.

        This function solves the generalized Sylvester equation AXB + CX = D for matrix X, where A, B, C, and D are given matrices. The solution uses:

        • Hessenberg decomposition of the matrix pair (A, C)

        • Complex Schur decomposition of matrix B

        • Back substitution to solve the transformed system

        Parameters:
        A - coefficient matrix A in the equation AXB + CX = D
        B - coefficient matrix B in the equation AXB + CX = D
        C - coefficient matrix C in the equation AXB + CX = D
        D - right-hand side matrix D in the equation AXB + CX = D
        Returns:

        solution matrix X satisfying AXB + CX = D