The solution to a nonsingular linear system Ax=b lies in a Krylov space whose dimension is the degree of the minimal polynomial of A (where A is a matrix, x & b are vectors). If this minimal polynomial of A has a low degree, a Krylov method has the potential of rapid convergence [1]. When solving a system of linear equations Ax=b, if the coefficient matrix A is large and sparse, the time requir...

A modified Polak-Ribière-Polyak conjugate gradient algorithm which satisfies both the sufficient descent condition and the conjugacy condition is presented. These properties are independent of the line search. The algorithms use the standard Wolfe line search. Under standard assumptions we show the global convergence of the algorithm. Numerical comparisons with conjugate gradient algorithms usi...

The Bayesian Information Criterion (BIC) was presented to obtain the appropriate structure, via the number of hidden nodes, and a new algorithm was proposed to improve the convergence speed of backpropagation training method. The algorithm was obtained by employing the conjugate gradient method to solve the nonlinear part in the weights of the hidden layers and the Kalman filter to solve the li...

The nonlinear conjugate gradient method is a very useful technique for solving large scale minimization problems and has wide applications in many fields. In this paper, we present a new algorithm of nonlinear conjugate gradient method with strong convergence for unconstrained minimization problems. The new algorithm can generate an adequate trust region radius automatically at each iteration a...

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step len...

In this paper, a new subspace adaptive algorithm, for blind separation of convolutive mixture, is proposed. This algorithm can be decomposed into two steps: At rst, the convolutive mixture will be reduced to an instantaneous mixture (memoryless mixture), using a second-order statistics criterion based on subspace approach. The second step consists on the separation of the residual instantaneous...

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing glo...

The basic conjugate gradient method for unconstrained optimal control problems was proposed by Lasdon et al. in [1]. The penalty function approach to the solution of inequality constrained optimal control problems has been considered in [2] and the clipping-off technique that solves optimal control problems with magnitude constraint on the control inputs is described in [3, 4]. The proposed alg...

2 [email protected] ________________________________________________________________________________ ABSTRACT We propose a new algorithm for removing a fast motion blur from an image. The term "iterative met hod" refers to a wide range of techniques which use successive approximations to obtain more accurate solutions .In this paper an attempt to solve systems of linear equations of the form ...