In this study integral form and new recursive formulas for Favard constants and some connected with them numeric and Fourier series are obtained. The method is based on preliminary integration of Fourier series which allows for establishing finite recursive representations for the summation. It is shown that the derived recursive representations are numerically more effective than known represe...

Abstract Many important computation problems can be specified by block recursive algorithms. For example, matrix transposition and fast Fourier transform are block recursive algorithms. In this paper, we present a methodology of VLSI circuit design for block recursive algorithms based on the tensor product theory. Matrix transposition and fast Fourier transform algorithms are designed and imple...

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...

We present matching upper and lower bounds for the “weak” polynomial degree of the recursive Fourier sampling problem from quantum complexity theory. The degree bound is h+ 1, where h is the order of recursion in the problem’s definition, and this bound is exponentially lower than the bound implied by the existence of a BQP algorithm for the problem. For the upper bound we exhibit a degree-h + ...

We revisit the oft-neglected ‘recursive Fourier sampling’ (RFS) problem, introduced by Bernstein and Vazirani to prove an oracle separation between BPP and BQP. We show that the known quantum algorithm for RFS is essentially optimal, despite its seemingly wasteful need to uncompute information. This implies that, to place BQP outside of PH [log] relative to an oracle, one needs to go outside th...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...