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In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-\sum_{i=1}^{m}A_{i}^*X^{-p_{i}}A_{i}=I$ with $p_{i}> 1$ is proposed, which does not depend on a good initial approximation to the solution of matrix equation.
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참고문헌 (20)
참고문헌 신청
W. N. Anderson Jr. / 1990 / Positive solutions to $X=A-BX^{-1}B^{\ast}$ / Linear Algebra Appl. 134:53~62
J. H. Avila Jr. / 1974 / The feasibility of continuation methods for nonlinear equations / SIAM J. Numer. Anal. 11:102~122
B. L. Buzbee / 1970 / On direct methods for solving Poisson's equations / SIAM J. Numer. Anal. 7:627~656
X. Duan / 2008 / On the nonlinear matrix equation $X-{\Sigma}^m_{i=1}A^{\ast}_iX^{{\delta}i}A_i$ = Q / Linear Algebra Appl. 429(1):110~121
J. C. Engwerda / 1993 / On the existence of a positive definite solution of the matrix equation $X+A^TX^{-1}A=I$ / Linear Algebra Appl. 194:91~108
J. H. Avila Jr. / 1974 / The feasibility of continuation methods for nonlinear equations / SIAM J. Numer. Anal. 11:102~122
B. L. Buzbee / 1970 / On direct methods for solving Poisson's equations / SIAM J. Numer. Anal. 7:627~656
X. Duan / 2008 / On the nonlinear matrix equation
J. C. Engwerda / 1993 / On the existence of a positive definite solution of the matrix equation
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