The main purpose of this paper is to find fuzzy root of fuzzy polynomials (if exists) by using Newton-Raphson method. The proposed numerical method has capability to solve fuzzy polynomials as well as algebric ones. For this purpose, by using parametric form of fuzzy coefficients of fuzzy polynomial and Newton-Rphson method we can find its fuzzy roots. Finally, we illustrate our approach by nu...

Variational inequalities, nonlinear programming, complementarity problems and other problems can be reduced to nonsmooth equations, for which some generalizations of Newton's method are known. The Newton path, as a natural generalization of the Newton direction, was suggested by D. Ralph for enlarging the convergence region (globalization) of Newton-Robinson's method in the nonsmooth case. We i...

We consider the problem of solving linear systems of equations with limited-memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory matrices. Using the proposed app...

Part 1. Measure Theory 1 1. Outer Measure: 9/23/14 1 2. The Lesbegue Measure: 9/30/14 5 3. Borel and Radon Measures: 10/2/14 8 4. Measurable Functions: 10/7/14 12 5. Convergence in Probability: 10/9/14 16 6. Back to Calculus: The Newton-Leibniz Formula: 10/14/14 20 7. Two Integration Theorems and Product Measures: 10/16/14 24 8. Product Measures and Fubini’s Theorem: 10/21/14 27 9. Besikovitch’...

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...

A new scheme for digital image correlation (DIC), i.e., short time series DIC (STS-DIC) is proposed. Instead of processing the original deformed speckle images individually, STS-DIC combines several adjacent deformed speckle images from a short time series and then processes the “averaged image”, for which deformation continuity over time is introduced. The deformation of several adjacent image...

Use of data assimilation techniques is becoming increasingly common across many application areas. The inverse Hessian (and its square root) plays an important role in several different aspects of these processes. In geophysical and engineering applications, the Hessian-vector product is typically defined by sequential solution of a tangent linear and adjoint problem; for the inverse Hessian, h...

Support vector machines (SVMs) have played a key role in broad classes of problems arising in various fields. Much more recently, SVMs have become the tool of choice for problems arising in data classification and mining. This paper emphasizes some recent developments that the author and his colleagues have contributed to such as: generalized SVMs (a very general mathematical programming framew...

We will present the Newton-Raphson algorithm, and the secant method. A MATLAB function for the Newton-Raphson method. The function.MATLAB has many tools that make this package well suited for numerical computations. The Newton-Raphson method for systems of nonlinear equations.The Newton-Raphson method, or Newton Method, is a powerful technique. Interesting is Section 3, where the birth of the N...

This paper describes an optimization method for minimization of quantization noise in ΣΔ-based RF transmitters. The aim of the method is to enable the use of reconstruction filters with wider passband, or alternatively, a lower switch-rate. The method uses a general representation of the ΣΔconverters in combination with a differentiable approximation of the quantizer. Based on this, a Monte-Car...