On the Steepest Descent Method for Matrix
نویسندگان
چکیده
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 node sequence has at most two points of accumulation. This knowledge is used to quantify the asymptotic convergence rate.
منابع مشابه
A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems
In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...
متن کاملHybrid steepest-descent method with sequential and functional errors in Banach space
Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...
متن کاملA new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations
In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...
متن کاملResidual norm steepest descent based iterative algorithms for Sylvester tensor equations
Consider the following consistent Sylvester tensor equation[mathscr{X}times_1 A +mathscr{X}times_2 B+mathscr{X}times_3 C=mathscr{D},]where the matrices $A,B, C$ and the tensor $mathscr{D}$ are given and $mathscr{X}$ is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...
متن کاملSteepest descent method for quasiconvex minimization on Riemannian manifolds
This paper extends the full convergence of the steepest descent algorithm with a generalized Armijo search and a proximal regularization to solve quasiconvex minimization problems defined on complete Riemannian manifolds. Previous convergence results are obtained as particular cases of our approach and some examples in non Euclidian spaces are given.
متن کاملOn the convergence speed of artificial neural networks in the solving of linear systems
Artificial neural networks have the advantages such as learning, adaptation, fault-tolerance, parallelism and generalization. This paper is a scrutiny on the application of diverse learning methods in speed of convergence in neural networks. For this aim, first we introduce a perceptron method based on artificial neural networks which has been applied for solving a non-singula...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008