分野別セミナー

We consider numerical methods for solving nonlinear matrix equations which are quadratic matrix equations, matrix polynomials and a class of nonlinear matrix equations of the form $X^{n}-f(X)=0$, where $f$ is a monotone matrix function defined on the cone of $k\times k$ positive definite real matrices. For solving many different types of nonlinear matrix equations, Newton's method is a very natural approach. We consider here how Newton steps can be applied for solving nonlinear matrix equations. Functional iterations and conjugate gradient methods are also considered. Finally, we show some numerical experiments.


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