The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes which elements mimic as well as possible the Chebyshev-Loba...

This pa per suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option`s continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is f...

Abstract—In Digital Signal Processing, one of the most important filter type is the FIR filter which can be designed via various methods. Window technique is the most important technique that is used to design the FIR filter. Apart from various window techniques, Dolph-Chebyshev window has the subject of importance for the design of the FIR filter in efficient way. In this paper, the design met...

We discuss a modification of the chained Rosenbrock function introduced by Nesterov. This function rN is a polynomial of degree four defined for x ∈ R. Its only stationary point is the global minimizer x∗ = (1, 1, . . . , 1) with optimal value zero. A point x in the box B := {x | −1 ≤ xi ≤ 1 for 1 ≤ i ≤ n} with rN (x) = 1 is given such that there is a continuous descent path within B that start...