Abstract. Computing the Fourier transform of a function in polar coordinates is an important building block in many scientific disciplines and numerical schemes. In this paper we present the pseudo-polar Fourier transform that samples the Fourier transform on the pseudo-polar grid, also known as the concentric squares grid. The pseudo-polar grid consists of equally spaced samples along rays, wh...

We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions e‘li (c( E Iw), the error decreases to 0 as n + a, if and only if d( is small enough to provide at least six points per wavelength. Second, the Lebesgue constant ,4. (supremum norm of the nth interpolation operator) ...

Lagrange interpolation estimates a function at a reference position χ from known values of the function at distinct non-uniformly spaced points x1, . . . , xn. Here, the corresponding n-point finite-difference formulas are derived to estimate derivatives up to order n − 1 at χ. A recurrence relation permits the errors to be determined to any accuracy as a Taylor series. The error coefficient mu...

We develop a bootstrap procedure for Lévy-driven continuous-time autoregressive (CAR) processes observed at discrete regularly-spaced times. It is well known that a regularly sampled stationary Ornstein–Uhlenbeck process [i.e. a CAR(1) process] has a discrete-time autoregressive representation with i.i.d. noise. Based on this representation a simple bootstrap procedure can be found. Since regul...

Seismic tomography traditionally inverts for velocity field on a regularly spaced and fixed-in-space model grid. Such an approach is not able to adequately describe pinchouts or wedge-shaped velocities as commonly seen at basin boundaries, faulted rock beds, and back-arc mantle wedges. A regularly spaced model grid also requires the use of a large number of model variables. This paper shows a d...

The sustainable management of groundwater resources needs quantitative information on its behaviors in space and time. With the availability of distributed models, which can handle large volume of data, the spatial information of groundwater at a grid pattern is not only useful but is necessary to get reliable results. Various methods, both simple and complicated, are available and are in use t...

The paper aims at the investigation of free word order. It concentrates on the relationship between (formal) dependencies and word order. The investigation is performed by means of a semi-automatic application of a method of analysis by reduction to Czech syntactically annotated data. The paper also presents the analysis of introspectively created Czech sentences demonstrating complex phenomena...

In the boundary representation (B-Rep) model, a three-dimensional (3D) surface is de ned by a set of ‘simpler surfaces’ called ‘patches’. Although there are many di erent ways to specify a patch, a common case is that of a 4-sided patch represented by a structured grid of points. For instance, this kind of data can easily be obtained from a CAD system, as it is the mapping of regularly spaced p...