This paper introduces a new class of quasi-Newton algorithms for unconstrained minimization in which no line search is necessary and the inverse Hessian approximations are positive definite. These algorithms are based on a two-parameter family of rank two, updating formulae used earlier with line search in self-scaling variable metric algorithms. It is proved that, in a quadratic case, the new ...

Newton-Cotes quadrature rules are based on polynomial interpolation in a set of equidistant points. They are very useful in applications where sampled function values are only available on a regular grid. Yet, these rules rapidly become unstable for high orders. In this paper we review two techniques to construct stable high-order quadrature rules using equidistant quadrature points. The stabil...

Let p(x1, ..., xm) = ∑ r1+···+rm=n ar1,...,rm ∏ 1≤i≤m x ri i be a homogeneous polynomial of degree n in m variables. We call such polynomial H-Stable if p(z1, ..., zm) 6= 0 provided that the real parts Re(zi) > 0 : 1 ≤ i ≤ m. It can be assumed WLOG that the coefficients ar1,...,rm := aR ≥ 0. This notion from Control Theory is closely related to the notion of Hyperbolicity intensively used in th...

This thesis discusses strategies for numerically solving a two dimensional integral. The difficulties here are due to numerous integrands and regions in R2. The transformation to units as the 2-simplex and the cube can simplify many integrands. An approach to arbitrary regions is to decompose them into easy ones as triangles and rectangles. For these regions formulas that approximate the two di...

Cervical Cancer is one of the ubiquitous forms of cancer afflicting the female population worldwide. A Colposcope is a self-illuminated microscope which acquires the image of the affected cervix and the image is known as a cervigram. The raw cervigram is preprocessed by removing the specular reflections and then the region of interest is sought. Before the image is made ready for implementing f...

New results relating the sparsity of nonhomogeneous polynomial systems and computation of their projection operator (a non-trivial multiple of the multivariate resultant) using Dixon's method are developed. It is demonstrated that Dixon's method of computing resultants, despite being classical, implicitly exploits the sparse structure of input polynomials. It is proved that the size of the Dixo...

Various methods of estimating eeective properties of composite materials require geometrical or topological information contained in the statistical three-point correlation functions. If these three-point correlation functions are measured using digital image processing techniques, the values are computed for a discrete set of admissible triangular arguments corresponding to triangles whose ver...

The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed ...

In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when initial energy E(u0) was subcritical (E(u0)<d), critical (E(u0)=d), and supercritical (E(u0)>d), with d being potential depth by using well method some differential inequalities. goal of paper to give result if ind...

One problem in appearance-based pose estimation is the need for many training examples, i.e. images of the object in a large number of known poses. Some invariance can be obtained by considering translations, rotations and scale changes in the image plane, but the remaining degrees of freedom are often handled simply by sampling the pose space densely enough. This work presents a method for acc...