A generalization of the steepest descent and other methods for solving a large scale symmetric positive definitive system Ax = b is presented. Given a positive integer m, the new iteration is given by xk+1 = xk −λ(xν(k))(Axk − b), where λ(xν(k)) is the steepest descent step at a previous iteration ν(k) ∈ {k, k−1, . . . , max{0, k−m}}. The global convergence to the solution of the problem is est...

In this paper we prove that the steepest descent of certain porous-medium type functionals with respect to the quadratic Wasserstein distance over a constrained (but not weakly closed) manifold gives rise to a nonlinear, nonlocal parabolic partial differential equation connected to the study of the asymptotic behavior of solutions for filtration problems. The result by Carlen and Gangbo on cons...

The present work deals with an improved back-propagation algorithm based on Gauss-Newton numerical optimization method for fast convergence. The steepest descent method is used for the back-propagation. The algorithm is tested using various datasets and compared with the steepest descent back-propagation algorithm. In the system, optimization is carried out using multilayer neural network. The ...

The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein “two-point step size” strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the Barzilai-Borwein strategy yields a method with an R-linear rate of convergence when it is employed to minimize a strongly convex quadratic. This paper exten...

In this paper an algorithm for optimizing coefficients of a Finite Impulse Response (FIR) filter, so as to reduce power dissipation of its implementation on a programmable Digital Signal Processor is presented. We then present an algorithm that optimizes coefficients so as to minimize the Hamming distance and signal toggling. Two such techniques „Steepest descent‟ and „Genetic Algorithm‟ are pr...

In this paper, we propose an efficient algorithm to solve the averaging problem on the Lorentz group O(n, k). Firstly, we introduce the geometric structures of O(n, k) endowed with a Riemannian metric where geodesic could be written in closed form. Then, the algorithm is presented based on the Riemannian-steepest-descent approach. Finally, we compare the above algorithm with the Euclidean gradi...

Central to the theoretical description of a chemical reaction is the reaction pathway. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted Cartesian coordinates that connects the transition state to reactants and products. In this work, a new integrator for the steepest descent pathway is presented. This method is a Hessian based predictor-corrector algori...