منابع مشابه
On the Steepest Descent Method for Matrix
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 with an interpolation process in which the...
متن کاملOn the Steepest Descent Method for Matrix
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 with an interpolation process in which the...
متن کاملSteepest descent method on a Riemannian manifold: the convex case
In this paper we are interested in the asymptotic behavior of the trajectories of the famous steepest descent evolution equation on Riemannian manifolds. It writes ẋ (t) + gradφ (x (t)) = 0. It is shown how the convexity of the objective function φ helps in establishing the convergence as time goes to infinity of the trajectories towards points that minimize φ. Some numerical illustrations are ...
متن کاملA limited memory steepest descent method
The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of th...
متن کاملA Generalization of the Steepest Descent Method for Matrix Functions∗
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 n...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1978
ISSN: 0021-9045
DOI: 10.1016/0021-9045(78)90080-1