Stencil computations are widely used to simulate the change of state physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal and Krylov subspace methods. In paper, we present two efficient parallel algorithms for performing li...

In multi-dimensional signal processing the Cliiord Fourier transform (CFT or in the 2-D case: quater-nionic Fourier transform/QFT) is a consequent extension of the complex valued Fourier transform. Hence, we need a fast algorithm in order to compute the transform in practical applications. Since the CFT is based on a corresponding Cliiord algebra (CA) and CAs are not commutative in general, we ...

We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to decompose the summation domain of into simpler components in a multiscale way. Existing fast algorithms are then applied to each component to obtain optimal compl...

In this thesis, we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating the irreducible representations of an inverse semigroup, and we use this method to prove that the problem of creating FFTs for inverse semigroups can ...

A group of algorithms is presented generalizing the fast Fourier transform to the case of nonin-teger frequencies and nonequispaced nodes on the interval [-r, r]. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires O(N log N + N-log(I...

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The are factored into a fixed number fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling shear transformations). these controls the trade-off between approximation accuracy computational complexity projecting on eigenspaces. w...

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideand-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to non-group semigroups.

— General guidelines for a new fast computation of blocklength 8m+4 DFTs are presented, which is based on a Laurent series involving matrices. Results of non-trivial real multiplicative complexity are presented for blocklengths N≤64, achieving lower multiplication counts than previously published FFTs. A detailed description for the cases m=1 and m=2 is presented.

Recent clinical and pre-clinical data demonstrate that adjuvant antimicrobial therapy is beneficial in cancer treatment. For the first time, an electrochemical method was proposed for the simultaneous determination of acyclovir (ACV) and methotrexate (MTX) at activated or electropretreated pencil graphite electrode (EPPEG). Their simultaneous determination was achieved by cyclic voltammetry (CV...