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A generalization of the steepest descent method for matrix functions. (English) Zbl 1171.65367

Summary: We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent to an interpolation process in which the node sequence has at most two points of accumulation. This knowledge is used to quantify the asymptotic convergence rate.

MSC:

65F10 Iterative numerical methods for linear systems
65F99 Numerical linear algebra
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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