An extension of a new multidimensional bisection method for minimizing function over simplex is proposed for solving nonlinear unconstrained minimization problem. The method does not require a differentiability of function, and is guaranteed to converge to the minimizer for the class of strictly unimodal functions. The computational results demonstrating an effectiveness of algorithm for minimi...

Let AABC be a triangle with vertices A, B, and C. It is "bisected" as follows: choose a/the longest side (say AB) of AABC, let D be the midpoint of AB, then replace AABC by two triangles aA.DC and ADBC. Let Ag| be a given triangle. Bisect Aqj into two triangles A¡¡ and Aj2. Next bisect each Aj(-, /= 1, 2, forming four new triangles A2j-, i = 1,2, 3,4. Continue thus, forming an infinite sequence...

No method for the computation of a reliable subset of the range of vector-valued functions is available today. A method for computing such inner approximations is proposed in the specific case where both domain and co-domain have the same dimension. A general sufficient condition for the inclusion of a box inside the image of a box by a continuously differentiable vector-valued is first provide...

The ability to time intervals confers organisms, including humans, with many remarkable capabilities. A common method for studying interval timing is classification, in which a subject must indicate whether a given probe duration is nearer a previously learned short or long reference interval. This task is designed to reveal the probe duration that is equally likely to be labeled as short or lo...

Based on Cuppen’s divide-and-conquer method [4] and bisection and multisection with the Sturm sequence evaluation coupled with inverse iteration [12, 8, 1], numerous parallel algorithms for solving the eigenvalue problem of real symmetric tridiagonal matrices Tn are presented in the literature [5, 3, 10, 7]. While Cuppen’s divide-and-conquer method achieves the better accuracy results in terms ...

We study whether bisection in visual grasp space (the region over which eye and hand can work together to grasp or touch objects) depends on fixation or on the method of judgment employed (the task). We determined observer bias and sensitivity for bisection judgments (in a fronto-parallel plane as well as along contours slanted in depth). Significant biases were found that varied across observe...

We investigate an algorithm derived based on the belief propagation method of Pearl [11] applied to the (Min-)Bisection problem under the standard planted solution model (or more precisely the Most Likely Partition problem under the same planted solution model). We first point out that the algorithm (without thresholding) is nothing but the standard power method for computing an eigenvector wit...

where the involved functions f and g are continuous (not necessarily differentiable) functions. The method is a tensor extension of the bisection method. Classical generalizations of bisection method are based on the topological degree, are called exclusion algorithms and are intended for separating all solutions of a system of equation in a given region [20,11,21,23]. More recent research line...

We present an n-dimensional marked bisection method for unstructured conformal meshes. devise the local refinement in adaptive applications. To this end, we propose a mesh marking pre-process and three stages. The marks initial conformingly. Then, first n−1 bisections, accumulates reverse order list of new vertices. In second stage, n-th bisection, uses reversed to cast bisected simplices as re...