In this paper, we give some sufficient and necessary conditions for discrete cosine operator functions on solid Banach function spaces to be chaotic or topologically transitive.

In this paper, a pricing method based on the Fourier-Cosine series expansion is introduced for equity-indexed annuities (EIAs) under Heston model. By means of expansion, density function underlying indexed recovered from its characteristic function, and then yields an efficient way EIAs pricing. To show accuracy method, numerical experiments, we provide results price classical Black-Scholes It ...

1. Error calculus 2 1.1. Ulp calculus 2 1.2. Relative error analysis 4 1.3. Generic error of addition/subtraction 4 1.4. Generic error of multiplication 5 1.5. Generic error of inverse 5 1.6. Generic error of division 6 1.7. Generic error of square root 7 1.8. Generic error of the exponential 7 1.9. Generic error of the logarithm 8 1.10. Ulp calculus vs relative error 9 2. Low level functions 9...

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative e...

In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258 (2015) 425-435; Abrarov & Quine, J. Math. Research, 7 (2) (2015) 163-174]. Here we show that it can also be utilized as a flexible and efficient tool in mathematical analysis. In particular, an application of the inco...

A L-estimate will be established for cosine series, considering the generalized Fomin-class Fφ, where φ is a function more general than the power function

Corresponding Author: Jitendra Nath Singh Department of Computer Science, Babasaheb Bhimrao Ambedkar University, Lucknow, India Email: [email protected] Abstract: Vector space model allows computing a continuous degree of similarity between queries and retrieved documents and then ranks the documents in increasing order of cosine (similarity) value. It computes cosine or similarity value us...

The goal of this work was to answer one simple question: given that the trigonometric functions take hundreds of clock cycles to execute on a Pentium IV, can they be computed faster, especially given that all Intel processors now have fast floating-point hardware? The streaming SIMD extensions (SSE/SSE2) in every Pentium III and IV provide both scalar and vector modes of computation, so it has ...

Some software libraries add special entry points to enable both the sine and cosine to be evaluated with one call for performance purposes. This paper proposes another method which does not involve new function names. By having the compiler front end recognize trigonometric function invocations, and replace them with a call to a common function which executes the code common to all the function...