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...
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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 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
The steepest descent method has a rich history and is one of the simplest and best known methods for minimizing a function. While the method is not commonly used in practice due to its slow convergence rate, understanding the convergence properties of this method can lead to a better understanding of many of the more sophisticated optimization methods. Here, we give a short introduction and dis...
متن کاملApproximate Steepest Coordinate Descent
We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach the efficiency of steepest coordinate descent (SCD), enabling an acceleration of a factor of up to n, the number of coordinates. In many practical applicatio...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2019
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1237/5/052014