Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots. What type of ...

Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using ...

Mathematics of Computation, Vol. 33, No. 148 (Oct., 1979), pp. 1251-1256 (6 pages) A polynomial representation of the hybrid methods for solving ordinary differential equations is presented. The ...

Abstract: This paper investigates the computational complexity involved when using Handelman relaxation method for solving multivariable polynomial optimization problems. In particular, the ...

It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton's identities. In this work, by further exploring ...

Abstract: We give an efficient implementation of the modified minimal polynomial extrapolation (MMPE) method for solving linear and nonlinear systems. We will show how to choose the auxiliary vectors ...

This is the PyTorch implementation of Legend-KINN, proposed by our paper "Legend-KINN: A Legendre Polynomial-Based Kolmogorov-Arnold-Informed Neural Network for Efficient PDE Solving", published in ...

In "CS364A: Algorithmic Game Theory," Tim Roughgarden states that any bimatrix, zero-sum game has a Nash Equilibrium that can be found within polynomial time. I do not have the skills to prove it, but ...