This paper presents a framework for synthesizing I/O-efficient out-of-core programs for block recursive algorithms , such as the fast Fourier transform and matrix transpositions. The programs are synthesized from tensor (Kronecker) product representations of algorithms. These programs are optimized for a striped two-level memory model where in the out-of-core data can have block-cyclic distribu...

A recursive construction is provided for sequence sets which possess good Hamming Distance and low Peak-to-Average Power Ratio (PAR) under any Local Unitary Unimodular Transform (including all one and multi-dimensional Discrete Fourier Transforms). An important instance of the construction identifies an iteration and specialisation of the Maiorana-McFarland (MM) construction.

We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O’Donnell and Servedio for regular decision trees [OS08]. We use this bound to obtain the first non-trivial lower bound on the parity decision tree complexity of the recursive majority function.

In this paper, we present three-grid Fourier analysis for multigrid methods. Due to the recursive structure of a multigrid iteration, this analysis can be deduced from the well-known two-grid Fourier analysis. The coarse grid correction part of multigrid algorithms can be more accurately evaluated with the three-grid analysis. We apply the analysis to several scalar equations and discretization...

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transfor...

In his article “Powerlist: A Structure for Parallel Recursion” Jayadev Misra wrote: “Many data parallel algorithms – Fast Fourier Transform, Batcher’s sorting schemes and prefix sum – exhibit recursive structure. We propose a data structure, powerlist, that permits succinct descriptions of such algorithms, highlighting the roles of both parallelism and recursion. Simple algebraic properties of ...

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consi...

in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

A simple recursive algorithm is proposed for reconstructing certain classes of two-dimensional objects from their autocorrelation functions (or equivalently from the modulus of their Fourier transforms-the phase-retrieval pioblem). The solution is shown to be unique in some cases. The objects contain reference points not satisfying the holography condition but satisfying weaker conditions. Incl...

A method is proposed for e ciently computing moving average lters in regular octagonal windows, as approximations to circular windows. The algorithm requires thirteen operations per pixel irrespective of window size and is faster than existing Fourier-based and recursive methods for all but the smallest windows. Further, new variance-weighted nonlinear lters are introduced, based on moving aver...