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‘Polynomial Solver Step by Step’ is a calculator, and, more importantly, a teaching tool. It is designed to help students of both basic and advanced levels. Basic Algebra functions: 1. Polynomial multiplication. 2. Polynomial long division with step by step explanation. 3. Algorithm for finding rational roots consisting of the following: a. Finding all possible rational roots. b. Eliminating the roots outside bounds. c. Performing polynomial long division for each of the roots. d. Adjusting bounds based on long division results if appropriate. Iterative polynomial solving algorithms for advanced-level students: 1. Durand-Kerner method. 2. Aberth method. 3. Newton method with both real and complex starting points. 4. Global (also known as "damped") Newton method with both real and complex starting points. 5. Laguerre method with both real and complex starting points. 6. Bairstow method. 7. Muller method. 8. Eigenvalues of ‘companion matrix’ (demonstration of QR algorithm for eigenvalue calculation is available in our “Matrix Solver Step by Step" app). Interactive graphs are available for: 1. Polynomial functions and their derivatives. 2. Aberth and Durand-Kerner method points on complex plane. 3. Newton, global Newton, Laguerre, and Muller algorithm steps. 4. Newton and global Newton method fractals / convergence images on complex plane 5. Laguerre method convergence images on complex plane 6 Bairstow method convergence images depending on initial approximation values. 7 Muller method convergence images depending on initial approximation values. (Images 4-7 have adjustable settings for area, resolution and shading). Links to online references are included. Please write to us if you like to have new features / chapters added! Next (closely related) project is an app that interpolates and approximates polynomials. We expect this will be available by March. Developers welcome any feedback, please write to us at graphmath@aol.com.
