asuresh213/root-finding-using-matrices

Implimentation of root-finding algorithm for non-linear problems using companion matrices

Root-Finding-Using-Matrices

Implimentation of root-finding algorithm for non-linear problems using companion matrices. Project completed as a part of final project for an undergraduate class - Computational Physics 1.

Motivation and Method:

Any root finding problem requires iterative techniques that converge to a single root; and is not particularly reliable to provide all roots of a function (even with different Initial conditions). In this project, we take the given root finding problem, and approximate it by its taylor series upto a provided tolerance. Following the taylor approximation, we create the so called companion matrix assosciated to the polynomial. The companion matrix M of a polynomial f has the property that the characteristic polynomial of M is f. Upon obtaining the companion matrix, we run M through an eigenvalue solver (a QR scheme) to obtain the eigenvalues of M - Through this process, by definition, we then obain the roots of $f$ to degree 2 less than the degree of the taylor approximation.