The Amended DSeSC Power Method for Polynomial Root-Finding

A Combinatorial Construction of High Order Algorithms for Finding Polynomial Roots of Known Multiplicity

We construct a family of high order iteration functions for finding polynomial roots of a known multiplicity s. This family is a generalization of a fundamental family of high order algorithms for simple roots that dates back to Schröder’s 1870 paper. It starts with the well known variant of Newton’s method B̂2(x) = x − s · p(x)/p′(x) and the multiple root counterpart of Halley’s method derived ...

TR-2002020: Inverse Power and Durand-Kerner Iterations for Univariate Polynomial Root-Finding

Polynomial Optimization Problems are Eigenvalue Problems

Abstract Many problems encountered in systems theory and system identification require the solution of polynomial optimization problems, which have a polynomial objective function and polynomial constraints. Applying the method of Lagrange multipliers yields a set of multivariate polynomial equations. Solving a set of multivariate polynomials is an old, yet very relevant problem. It is little k...

TR-2011004: Acceleration of Newton's Polynomial Factorization: Army of Constraints, Convolution, Sylvester Matrices, and Partial Fraction Decomposition

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

A root-MUSIC algorithm for non circular sources

We present in this paper a new direction finding algorithm for non circular sources that is based on polynomial rooting. Due to the non circularity characteristics of the impinging sources, the proposed method is able to handle more sources than sensors. By using a polynomial rooting instead of a searching technique the method is limited to linear uniformly spaced arrays. However, polynomial ro...