Calculating the spectral function of two dimensional systems is arguably one most pressing challenges in modern computational condensed matter physics. While efficient techniques are available lower dimensions, present insurmountable hurdles, ranging from sign problem quantum Monte Carlo (MC), to entanglement area law tensor network based methods. We hereby a variational approach on Chebyshev e...

We characterize polynomial decomposition fn = r ◦ q with r, q ∈ C[x] of perturbed Chebyshev polynomials defined by the recurrence f0(x) = b, f1(x) = x− c, fn+1(x) = (x− d)fn(x)− afn−1(x), n ≥ 1, where a, b, c, d ∈ R and a > 0. These polynomials generalize the Chebyshev polynomials, which are obtained by setting a = 1/4, c = d = 0 and b ∈ {1, 2}. At the core of the method, two algorithms for pol...

BP decoding algorithm is a high-performance low-density parity-check (LDPC) code decoding algorithm, but because of its high complexity, it can’t be applied to the high-speed communications systems. So in order to further reduce the implementation complexity with the minimum affection to the system performance, , we proposed a BP algorithm based on Chebyshev polynomial fitting for its good appr...

ANEHP-Alpha, a new analog evolvable hardware (EHW) platform based on AN231E04 field programmable analog array (FPAA) device is described and a fourth-order Chebyshev filter is evolved on it. AN231E04 is one of the latest models of the FPAA series based on switched capacitor technology from Anadigm Corporation. Reaping the benefit of its flexible dynamic reconfiguration ability and function-leve...

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier–Stokes equations on a disk with no-slip boundary conditions is described. The vorticitystream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier–Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implic...

Robust polynomial rootfinders can be exploited to compute the roots on a real interval of a nonpolynomial function f(x) by the following: (i) expand f as a Chebyshev polynomial series, (ii) convert to a polynomial in ordinary, series-of-powers form, and (iii) apply the polynomial rootfinder. (Complex-valued roots and real roots outside the target interval are discarded.) The expansion is most e...

In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie groupand exponential time integrators for differential equations, we will in the first part of the article present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetri...