This items very briefly describes the concept of factorization.
The Cayley-Hamilton Theorem
Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
This collection of modules considers factoring very high degree polynomials with random coefficients. It looks particularly at the Lindsey-Fox algorithm and describes the program written by Jim Fox.
Horner's method is a standard minimum arithmetic method for evaluating and deflating polynomials. It can also efficiently evaluate various order derivatives of a polynomial, therefore is often used as part of Newton's method. This note tries to develop the various techniques called Horner's method, nested evaluation, and synthetic division in a common framework using a recursive structure and difference equations. There is a similarity to GOERtzel's algorithm for the DFT, Z-transform inversion by division, and Pade's and Prony's methods. This approach also allows a straight forward explanation of "stability" or numerical errors of the algorithms. Matlab implementations are given. This note came from the work of the "Polynomial Club" at Rice: Burrus, Fox, Sitton, and Treitel.
Lagrange's interpolation formula is a simple and clever method for finding the unique polynomial of order L that exactly passes through L+1 distinct samples of a signal.
The program which implements the Lindsey-Fox algorithm that factors high degree polynomial is organized in three stages. Jim Fox is the primary author and architect of the program.
Factoring a high degree polynomial has been considered a difficult problem since the beginning of mathematics. We describe the strategies used to attack this problem. The results are from a group called the "Polynomial Club" (Jim Fox, Sidney Burrus, Gary Sitton, and Sven Treitel)
This module describes the method of partial fraction expansion, in which a ratio of polynomials can be split into a sum of small polynomials.The Heaviside cover-up method is discussed in detail with examples.Finding a partial fraction expansion in matlab is also discussed.
This module will introduce rational functions and describe some of their properties. In particular, it will discuss how rational functions relate to the z-transform and provide a useful tool for characterizing LTI systems.
