Related papers: On Some New Applications to Newton-Raphson Method
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
A novel methodology to efficiently approximate the Hessian for numerical shape optimization is considered. The method enhances operator symbol approximations by including body fitted coordinates and spatially changing symbols in a semi…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
In this paper we show how to approximate ("learn") a function f, where X and Y are metric spaces.
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
This paper presents a methodology for finding numerically, by means of curve-following, all real solutions of a general system of $n$ nonlinear equations in $n$ unknowns, within a given $n$-dimensional box. The main idea behind our method…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
In the Area Labeling Problem one is after placing the label of a geographic area. Given the outer boundary of the area and an optional set of holes. The goal is to find a label position such that the label spans the area and is conform to…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…