Related papers: An efficient method for the computation of the Fei…
In this paper we will algorithmically prove the local and global epsilon constant conjectures for all fields of absolute degree lower or equal to 15. To this end we will present an efficient algorithm for the computation of local…
We present a parallel algorithm for calculating very large determinants with arbitrary precision on computer clusters. This algorithm minimises data movements between the nodes and computes not only the determinant but also all minors…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work…
We provide an efficient method to evaluate the generalized Stieltjes constants $\gamma_n(a)$ numerically to arbitrary accuracy for large $n$ and $n \gg |a|$ values. The method uses an integral representation for the constants and evaluates…
The generalized Stieltjes constants $\gamma\_n(v)$ are, up to a simple scaling factor, the Laurent series coefficients of the Hurwitz zeta function $\zeta(s,v)$ about its unique pole $s = 1$. In this work, we devise an efficient algorithm…
An investigation of the comparative efficiency of the different methods in which {\pi} is cal- culated. This thesis will compare and contrast five different methods in calculating {\pi} by first deriving the various proofs to each method…
We propose a new method to accelerate the convergence of optimization algorithms. This method simply adds a power coefficient $\gamma\in[0,1)$ to the gradient during optimization. We call this the Powerball method and analyze the…
We present a deterministic algorithm, which, for any given 0< epsilon < 1 and an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln…
In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations…
For two unknown mixed quantum states $\rho$ and $\sigma$ in an $N$-dimensional Hilbert space, computing their fidelity $F(\rho,\sigma)$ is a basic problem with many important applications in quantum computing and quantum information, for…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
The fidelity estimation between two quantum states is crucial for quantum computation and information science. However, an efficacious method for this, especially for mixed states and higher-dimensional density matrices, remains elusive.…
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In…