In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an effective method for increasing classification accuracy algorithms. This paper introduces a family one-parameter functions improving SVM classification. proposed function consists ...

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...

We describe the computations of some intrinsic constants associated to an n-dimensional normed space V, namely the N -th “allometry” constants κ∞(V) := inf { ‖T‖ · ‖T ′‖, T : `∞ → V, T ′ : V → `∞, TT ′ = IdV } . These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our computations for some low-dimensional spaces such as sequenc...

Let φ(n) be any function which grows more slowly than exponentially in n, i.e., limsup n→∞ φ(n)1/n ≤ 1. There is a double trigonometric series whose coefficients grow like φ(n), and which is everywhere convergent in the square, restricted rectangular, and one-way iterative senses. Given any preassigned rate, there is a one dimensional trigonometric series whose coefficients grow at that rate, b...

We rigorously study a novel type of trigonometric Fourier collocation methods for solving multi-frequency oscillatory second-order ordinary differential equations (ODEs) q′′(t) + Mq(t) = f(q(t)) with a principal frequency matrix M ∈ Rd×d. If M is symmetric and positive semi-definite and f(q) = −∇U(q) for a smooth function U(q), then this is a multi-frequency oscillatory Hamiltonian system with ...

A class of cubic Bézier-type curves based on the blending of algebraic and trigonometric polynomials, briefly CAT Bézier curves, is presented in this paper. The CAT Bézier curves retain the main superiority of cubic Bézier curves. The CAT Bézier curves can approximate the Bézier curves from the both sides, and the shapes of the curves can be adjusted totally or locally. With the shape parameter...

The following problem originated from a question due to Paul Turán. Suppose Ω is a convex body in Euclidean space R or in T, which is symmetric about the origin. Over all positive definite functions supported in Ω, and with normalized value 1 at the origin, what is the largest possible value of their integral? From this Arestov, Berdysheva and Berens arrived to pose the analogous pointwise extr...

The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation. 1. Outline and introduction Recently, in an attempt to prove, through the Cauchy residue method, Dougall’s theorem (Dougall [6, 1907], se...

In the present article, we have established a result on degree of approximation function in Besov space by (N; rn)- mean Trigonometric Fourier series