New Optimization Algorithms to Calculate Roots of Polynomials

[Namir]

Hi All,

I posted here a PDF file than contains an article I wrote about two new algorithms that use optimization to calculate real and complex roots for real-coefficient polynomials. The algorithms are:

1) Newton-Vieta method that uses Newton's method to obtain teh real roots of the polynomial and then optimizes the Vieta Formulas to obtain the pair of conjugate complex roots from the deflated polynomial.

2) Quasi Lin-Bairstow method. A method that, like Lin-Bairstow, uses optimization to extract quadratic polynomials from a bigger polynomial using optimization. The extracted quadratic polynomials have either a pair of real roots or a pair of conjugate complex roots.

Enjoy!

Namir