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Tsung-Ming Hwang

2007-05-11
14:10:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In 2006, Lin and Xu proposed a structure-preserving doubling algorithm (SDA) for solving the nonlinear matrix equation $X + A^T X^{-1} A = Q$ (with $Q>0$). The SDA was proven to beconvergent quadratically to the maximal solution $X_{+}$ when all eigenvalues of $X_{+}^{-1}A$ lie inside the unit circle. In this talk, we will show that SDA converges linearly to a symmetric solution $X_{+}$ when all eigenvalues of $X_{+}^{-1} A$ are inside or on the unit circle and the partial multiplicity of each unimodular eigenvalue is half of the partial multiplicity of the corresponding unimodular eigenvalue of the associated symplectic pencil.