Newton's method for symmetric and bisymmetric solvents of the nonlinear matrix equations
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One of the interesting nonlinear matrix equations is the qua-dratic matrix equation defined by Q(X) = AX2 + BX + C = 0, where X is a n×n unknown real matrix, and A,B and C are n×n givenmatrices with real elements. Another one is the matrix polynomial P(X) = A0Xm + A1Xm−1 + · · · + Am = 0, X,Ai 2 Rn×n. Newton’s method is used to find the symmetric and bisymmetric solventsof the nonlinear matrix equations Q(X) and P(X). The method does notdepend on the singularity of the Fr´echet derivative. Finally, we give somenumerical examples.
Abstract
One of the interesting nonlinear matrix equations is the qua-dratic matrix equation defined by Q(X) = AX2 + BX + C = 0, where X is a n×n unknown real matrix, and A,B and C are n×n givenmatrices with real elements. Another one is the matrix polynomial P(X) = A0Xm + A1Xm−1 + · · · + Am = 0, X,Ai 2 Rn×n. Newton’s method is used to find the symmetric and bisymmetric solventsof the nonlinear matrix equations Q(X) and P(X). The method does notdepend on the singularity of the Fr´echet derivative. Finally, we give somenumerical examples.
참고문헌 (12)
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