Abstract Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task institutions, and its speed-up will provide a large business impact. Recently, applications quantum computing to problems have been started be investigated. In this paper, we first propose algorithm for option pricing. This method performs the app...

Lagrange interpolation is a classical method for approximating a continuous function by a polynomial that agrees with the function at a number of chosen points (the “nodes”). However, the accuracy of the approximation is greatly influenced by the location of these nodes. Now, a useful way to measure a given set of nodes to determine whether its Lagrange polynomials are likely to provide good ap...

A discrete Fourier analysis on the fundamental domain Ωd of the d-dimensional lattice of type Ad is studied, where Ω2 is the regular hexagon and Ω3 is the rhombic dodecahedron, and analogous results on d-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas o...

In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...

An efficient method for the design of the half-band filter is described. Both the characteristics of the time response and the frequency response of the half-band filter are fully utilised to reduce the computation time and to increase the computation accuracy. The algorithm is based on the Chebyshev approximation criterion and uses only odd-symmetry polynomials for frequency interpolation to m...

We implement in Matlab a Gauss-like cubature formula on bivariate domains whose boundary is a piecewise smooth Jordan curve (curvilinear polygons). The key tools are Green’s integral formula, together with the recent software package chebfun to approximate the boundary curve close to machine precision by piecewise Chebyshev interpolation. Several tests are presented, including some comparisons ...

Best L1 approximations of the Heaviside function in Chebyshev and weak-Chebyshev spaces has a Gibbs phenomenon. It has been shown in the nineties for the trigonometric polynomial [1] and polygonal line cases [2]. By mean of recent results of characterization of best L1 approximation in Chebyshev and weak-Chebyshev spaces [3] that we recall, this Gibbs phenomenon can also be evidenced in the pol...