Polynomial Solver Step by Step

‘Polynomial Solver Step by Step’ performs and teaches both analytical and numerical methods of solving polynomials.

Numerical methods include:

1. Eigenvalues of ‘companion matrix’.
2. Durand-Kerner method.
3. Aberth method.
4. Newton method with both real and complex x0.
5. Global (also known as "damped") Newton method with both real and complex x0.

This app demonstrates the composition of ‘companion matrix’ and rationale for matrix eigenvalues being equal to polynomial solutions.
The algorithm for eigenvalue calculation is explained in our ‘Matrix Solver Step by Step’ app.
Complex plane graphs for starting points, intermediate points, and solutions for methods 2 and 3 are available.

Analytical methods include an algorithm consisting of the following steps:

1. Finding all possible rational roots.
2. Eliminating the roots outside bounds.
3. Performing / demonstrating polynomial long division for each of the roots.
4. Adjusting bounds based on long division results if appropriate.

Available graphs:
1. Polynomial functions and their derivatives.
2. Aberth and Durand-Kerned method points on complex plane.
3. Newton and global Newton algorithm steps.
4. Newton and global Newton fractals on complex plane with adjustable settings for area, resolution and shading.

Unlike our previous ‘Polynomials and Linear Systems’ app, this one focuses on Polynomial functions only and has new features:
1. Includes Durand-Kerner, Aberth and Newton methods.
2. Demonstrates solution steps.
3. Solves polynomials of up to 20 degrees.
(The ‘Polynomials and Linear Systems’ app will eventually be phased out)

New features will be added to ‘Polynomial Solver Step by Step’ in the near future!

Developers welcome any feedback, please write to us at graphmath@aol.com.