Interpolation with circular basis functions

In this paper we consider basis function methods for solving the problem of interpolating data over distinct points on the unit circle. In the special case where the points are equally spaced we can appeal to the theory of circulant matrices which enables an investigation into the stability and accuracy of the method. This work is a further extension and application of the research of Cheney, Light and Xu ([W.A. Light and E.W. Cheney, J. Math. Anal. Appl., 168:110–130, 1992] and [Y. Xu and E.W. Cheney, Computers Math. Applic., 24:201–215, 1992]) from the early nineties

A Duchon framework for the sphere

In his fundamental paper (RAIRO Anal. Numer. 12 (1978) 325) Duchon presented a strategy for analysing the accuracy of surface spline interpolants to sufficiently smooth target functions. In the mid-1990s Duchon's strategy was revisited by Light and Wayne (J. Approx. Theory 92 (1992) 245) and Wendland (in: A. Le Méhauté, C. Rabut, L.L. Schumaker (Eds.), Surface Fitting and Multiresolution Methods, Vanderbilt Univ. Press, Nashville, 1997, pp. 337–344), who successfully used it to provide useful error estimates for radial basis function interpolation in Euclidean space. A relatively new and closely related area of interest is to investigate how well radial basis functions interpolate data which are restricted to the surface of a unit sphere. In this paper we present a modified version Duchon's strategy for the sphere; this is used in our follow up paper (Lp-error estimates for radial basis function interpolation on the sphere, preprint, 2002) to provide new Lp error estimates (p[1,∞]) for radial basis function interpolation on the sphere

On the accuracy of surface spline interpolation on the unit sphere

This paper considers a novel modification to the surface splines that have previously been used on the unit sphere. The surface splines considered are a natural analogue of surface splines in IRd and possess a unique Fourier expansion in terms of an orthonormal basis of spherical harmonics. Knowing the decay of the associated Fourier coefficients is important because they enable error estimates for spherical interpolation. In this paper we explicitly compute the Fourier coefficients of the surface splines and employ a recent theoretical result [8] to provide a useful error bound. We illuminate our theoretical findings by performing numerical experiments on the sphere and also on the hemisphere

A numerical study of radial basis function based methods for option pricing under one dimension jump-diffusion model

The aim of this paper is to show how option prices in the Jump-diffusion model can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the Ameri- can put and the European vanilla call/put options on dividend-paying stocks in the Merton and Kou Jump-diffusion models. The radial basis function we select is the Cubic Spline. We also propose a simple numerical algorithm for finding a finite computational range of a global integral term in the PIDE so that the accuracy of approximation of the integral can be improved. Moreover, the solution functions of the PIDE are approximated explicitly by RBFs which have exact forms so we can easily compute the global intergal by any kind of numerical quadrature. Finally, we will also show numerically that our scheme is second order accurate in spatial variables in both American and European cases

Potential economic impacts of providing for Aquaculture Management Areas in Canterbury

This research estimates the commercial costs and benefits associated with selected aquaculture projects in the Canterbury region. Mussel farming employment will most likely be generated in coastal communities that at present have few employment opportunities. These communities are likely to profit as well from increased infrastructure needs for the marine farming enterprise. Any development in the marine farming industry will take many years to reach full potential. This means that the costs and benefits from increased marine farming activities will be staggered over a number of years. It is acknowledged that the gains might be achieved at different locations than the losses occur. The effects on other stakeholders are often uncertain.Mussel farming, economic impact, scenarios, Agribusiness, Agricultural and Food Policy, Crop Production/Industries, Environmental Economics and Policy, Farm Management, Land Economics/Use,

Radial basis functions for the sphere

In this paper we compute the ultraspherical series expansions for the more commonly used radial basis functions. In several special cases we provide asymptotic estimates for the decay rate of the coefficients involved. knowledge of the decay rate of these coefficients is useful because they enable error estimates for spherical interpolation

An Adversarial Super-Resolution Remedy for Radar Design Trade-offs

Radar is of vital importance in many fields, such as autonomous driving, safety and surveillance applications. However, it suffers from stringent constraints on its design parametrization leading to multiple trade-offs. For example, the bandwidth in FMCW radars is inversely proportional with both the maximum unambiguous range and range resolution. In this work, we introduce a new method for circumventing radar design trade-offs. We propose the use of recent advances in computer vision, more specifically generative adversarial networks (GANs), to enhance low-resolution radar acquisitions into higher resolution counterparts while maintaining the advantages of the low-resolution parametrization. The capability of the proposed method was evaluated on the velocity resolution and range-azimuth trade-offs in micro-Doppler signatures and FMCW uniform linear array (ULA) radars, respectively.Comment: Accepted in EUSIPCO 2019, 5 page

Custer\u27s Last Fight At Little Big Horn

Dubbed highly innacurate (O\u27Keefe 2012), the work is interesting as an advertising specimen. Contains footnotes by the Hartford Lunch Company with sayings about their business practices and ethics--for example, Waste is an indirect tax. We pay for it through advanced prices. HARTFORD LUNCH CO. (page 23).https://red.mnstate.edu/rarebooks/1000/thumbnail.jp

L_(p)-error estimates for radial basis function interpolation on the sphere

In this paper we review the variational approach to radial basis function interpolation on the sphere and establish new Lp-error bounds, for p[1,∞]. These bounds are given in terms of a measure of the density of the interpolation points, the dimension of the sphere and the smoothness of the underlying basis function