We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge globally and linearly (i.e., the error decays exponentially), with explicit rates. In special cases, we obtain stochastic block variants of several quasiNewton upda...

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Conv...

Huber, Krokhin, and Powell (2013) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the three-value domain, and Huber and Krokhin (2014) showed the oracle tractability of minimization of skew-bisubmodular functions. Fujishige, Tanigawa, and Yoshida (2014) also showed a min-...

In this paper, we propose a natural way to extend a bivariate Powell–Sabin (PS) B-spline basis on a planar polygonal domain to a PS B-spline basis defined on a subset of the unit sphere in R3. The spherical basis inherits many properties of the bivariate basis such as local support, the partition of unity property and stability. This allows us to construct a C1 continuous hierarchical basis on ...

cables have always been under consideration as a structural element because of important features such as large strength to weight ratios and long spans. their equilibrium analysis is an important issue in this regard. but this analysis involves highly nonlinear equations arising from large deformations and material nonlinearity. different methods have been under use for numerical analysis of s...

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulpi...

This paper reports the study results on neural network training algorithm of numerical optimization techniques multiface detection in static images. The training algorithms involved are scale gradient conjugate backpropagation, conjugate gradient backpropagation with Polak-Riebre updates, conjugate gradient backpropagation with Fletcher-Reeves updates, one secant backpropagation and resilent ba...

This paper presents a new approach based on a Two-Stage Linear Discriminant Analysis (Two-Stage LDA) and Conjugate Gradient Algorithms (CGAs) for face recognition. A Two-Stage LDA technique is proposed that utilises the null space of the sample covariance matrix as well as using the range space of the between-class scatter matrix to extract discriminant information. Classic Back Propagation (BP...