Calculation of zeros of a real polynomial using scaling of its coefficients

Abstract

A composite method has been presented for finding the zeros of a real polynomial. The method has proved itself to be fast and successful in determining the zeros of polynomials with a greater degree of accuracy. It has been particularly successful in efficiently calculating multiple zeros which cause trouble for most root-finding algorithms. The composite algorithm consists of two basic parts. First, the input coefficients are scaled to minimize their variation of orders of magnitude. Secondly, the scaled polynomial is then factored, through the deflation process by extracting a quadratic factor each time. The calculated zeros are then scaled by the scale factor. The method has been tested on various well and ill conditioned polynomials and with multiple zeros. The method has proved to be computationally efficient, accurate and fast.

Keywords:

• Scale factor
• Polynomial scaling
• Routh Array-type algorithm
• Quadratic factors
• iterations
• deflation
• zeros

C.R. CATEGORIES::

• 5.15
• 5.1