Abstract—We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach t...

In this paper, we consider an algorithm that efficiently evaluates a trigonometric polynomial at arbitrarily spaced nodes. It is based on the approximation of the polynomial by a function we can evaluate easily. We are particularly interested in the case where we interpolate the trigonometric polynomial using high-order cardinal interpolation kernels known as Z-splines, which we construct and s...

Asymptotic forms of the Hilbert-Scmidt and Hilbert norms of positive definite Töplitz matrices QN = (b(j − k)) N−1 j,k=0 as N → ∞ are determined. Here b(j) are consequent trigonometric moments of a generating non-negative mesure dσ(θ) on [−π, π]. It is proven that σ(θ) is continuous if and only if any of those contributions is o(N). Analogous criteria are given for positive integral operators w...

7 Trigonometric Identities, Complex Exponentials and Periodic Sequences 26 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 26 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 28 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 29 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 31 7.5 The Exponential of a Complex Numbe...

List of included articles [1] H. Rauhut. Random sampling of sparse trigonometric polynomials. Appl. Comput. [2] S. Kunis and H. Rauhut. Random sampling of sparse trigonometric polynomials II-orthogonal matching pursuit versus basis pursuit. [3] H. Rauhut. Stability results for random sampling of sparse trigonometric polynomi-als. [4] H. Rauhut. On the impossibility of uniform sparse reconstruct...

We will prove some inequalities among trigonometric quantities of two and three operators. In particular, we will establish an inequality among joint trigonometric quantities of two operators and trigonometric quantities of each operator. As a corollary, we will find an upper bound and a lower bound for the total joint antieigenvalue of two positive operators in terms of the smallest and larges...

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape α(t) and β(t) are constructed in a space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots previous work as special cases. Sufficient conditions concerning to guarantee construction given, three specific examples related application...