It is shown that the four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation, and topological epsilon algorithm, when applied to linearly generated vector sequences, are Krylov subspace methods, and are equivalent to some well known conjugate gradient type methods. A unified recursive method that includes the con...

Two new nonlinear spectral conjugate gradient methods for solving unconstrained optimization problems are proposed. One is based on the Hestenes and Stiefel (HS) method and the spectral conjugate gradient method. The other is based on a mixed spectral HS-CD conjugate gradient method, which combines the advantages of the spectral conjugate gradient method, the HS method, and the CD method. The d...

Recently, important contributions on convergence studies of conjugate gradient methods have been made by Gilbert and Nocedal [6]. They introduce a “sufficient descent condition” to establish global convergence results, whereas this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, [6] hints that the sufficient descent condition, which was enforced by their ...

A list of technical reports, including some abstracts and copies of some full reports may be found at: Object test coverage using finite state machines. September 1995. On balancing workload in a highly mobile environment. August 1995. Error analysis of a partial pivoting method for structured matrices. June 1995. Abstract In this expository paper, we survey some of the latest developments on u...

We present an efficient and accurate variant of the conjugate gradient method for solving families of shifted systems. In particular we are interested in shifted systems that occur in Tikhonov regularization for inverse problems since these problems can be sensitive to roundoff errors. The success of our method in achieving accurate approximations is supported by theoretical arguments as well a...

We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditioned ...

Training of artificial neural networks is normally a time consuming task due to iterative search imposed by the implicit nonlinearity of the network behavior. To tackle the supervised learning of multilayer feed forward neural networks, the backpropagation algorithm has been proven to be one of the most successful neural network algorithm. Although backpropagation training has proved to be effi...

where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.