Suppose pp is an odd prime and aa is a quadratic residue modulo pp. Cipolla's algorithm shows that b:=x(p+1)/2mod(x2−tx+a)b:=x(p+1)/2mod(x2−tx+a) such that b2=ab2=a for some irreducible polynomial x2−tx+a
of generally known conventional algorithm for calculating a square root using Newton's method converging and finding an answer by use of the division, wherein it is difficult to apply the algorithm to calculation of a larger digit number or to apply it to calculation of a cubic or more root...
Root MUSIC (Multiple Signal Classification) Algorithm 1. Introduction In the previous discussion, we introduced the MUSIC algorithm, whose core idea is to traverse a sufficient number of manifold vectors and find the peaks in the MUSIC spectrum, as shown in Equation (1): (1)PMUSIC(k)=1aH(...
The old Babylonian algorithm is an ancient method for computing various mathematical values. One of its notable applications is in calculating the square root of a number. This algorithm works by making an initial guess and then refining it through a series of iterations. For example, to find ...
The convergence rate reaches quadratic in a close neighborhood of a root. Whether Newton-Raphson algorithm converges depends on the nonlinear equations and the initial guess of the solution. As an example, finding the root of a polynomial by Newton-Raphson algorithm can be realized by the ...
Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently pre...
Many existing algorithms require the number of clusters to be specified as part of the user parameters required for running the algorithm. Determining this parameter apriori is known as automatic clustering, and it has continued to attract more attention since, in many of the recent algorithms, ...
Can use this algorithm for finding Floyd’s cycle as it can find duplicates in a sequence of integers from x1, x2, x3 … where x belongs to integer where sequence is defined by x1=2, x(i+1)=f(xi)= (Square of (xi) + 1). The elliptic curve discrete logarithmic problem can be ...
Reducing the measurement effort that is made for identification of parameters is an important task in some fields of technology. This work focuses on calibration of functions running on the electronic control unit (ECU), where measurements are the main e
A special type of hierarchical algorithms that are most appropriate for handling large data sets is discussed. The need for such algorithms stems from a number of applications, such as Web mining and bioinformatics. View chapter Book 2009, Pattern Recognition (Fourth Edition)Sergios Theodoridis, ...