Related papers: Approximation of fuzzy numbers by convolution meth…
Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…
Digital image segmentation is the process of assigning distinct labels to different objects in a digital image, and the fuzzy segmentation algorithm has been successfully used in the segmentation of images from a wide variety of sources.…
The work presents an extension of the fuzzy approach to 2-D shape recognition [1] through refinement of initial or coarse classification decisions under a two pass approach. In this approach, an unknown pattern is classified by refining…
In this paper, we firstly introduce nonlinear truncated Baskakov operators on compact intervals and obtain some direct theorems. Also, we give the approximation of fuzzy numbers by truncated nonlinear Baskakov operators.
In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the…
Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…
Convolution and cross-correlation are the basis of filtering and pattern or template matching in multimedia signal processing. We propose two throughput scaling options for any one-dimensional convolution kernel in programmable processors…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution. First additive and multiplicative…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Fuzzy numbers are commonly represented with fuzzy sets. Their objective is to better represent imprecise data. However, operations on fuzzy numbers are not as straightforward as maths on crisp numbers. Commonly, the Zadeh's extension rule…
It is well known that the set of origami constructible numbers is larger than the classical straight-edge and compass constructible numbers. However, the Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the…
As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…