Related papers: Efficient resolution of the Colebrook equation
We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
This study concerns the efficiency of time-spectral methods for numerical solution of differential equations. It is found that the time-spectral method GWRM demonstrates insensitivity to stiffness and chaoticity due to the implicit nature…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
In this paper, we develop efficient and accurate algorithms for evaluating $\varphi(A)$ and $\varphi(A)b$, where $A$ is an $N\times N$ matrix, $b$ is an $N$ dimensional vector and $\varphi$ is the function defined by…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We present an algorithm to solve the CASSCF linear response equations that is both simple and efficient. The algorithm makes use of the well established symmetric and antisymmetric combinations of trial vectors, but further orthogonalizes…