Horner's Method

Horner's Method (Ruffini-Horner Scheme) for evaluating polynomials including a brief history, examples, Ruffini's Rule with derivatives, and root finding using Newton-Horner. Example code on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:11 - History 1:33 - TLDR 1:47 - Function vs Polynomial 2:23 - Horner's Method 2:50 - Horner's Method Examples 3:36 - Synthetic Division 4:32 - Ruffini's Rule Main Idea 4:58 - Ruffini's Rule 5:34 - Derivative with Ruffini's Rule 6:00 - Derivative Example 6:27 - Polynomial Root Finding 6:36 - Algebraic Root Finding 6:59 - Rational Root Theorem 7:35 - Newton-Horner Method 8:23 - Newton-Horner Example 9:11 - Summary 9:36 - Thank You Further Viewing: Newton's Method https://youtu.be/E24zUEKqgwQ Laguerre's Method https://youtu.be/blOARV4lnIM Newton Fractals https://youtu.be/MWD2A0Vg2V0 Durand-Kerner Method https://youtu.be/5JcpOj2KtWc Aberth-Ehrlich Method https://youtu.be/XIzCzfMDSzk Bairstow's Method https://youtu.be/iUGEk6kngFw References: Horner's paper https://www.jstor.org/stable/107508 Ruffini https://doi.org/10.1090/S0002-9904-1911-02072-9 Chemla's paper https://doi.org/10.1017/S0957423900001235 Qin Jiushao http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.454.4986&rep=rep1&type=pdf#page=169 Sharaf al-Dīn al-Tūsī https://doi.org/10.1016/0315-0860(89)90099-2 Jia Xian https://www.math.vt.edu/people/brown/doc/fibo_number.pdf Yong's paper https://sms.math.nus.edu.sg/smsmedley/Vol-14-1/The%20development%20of%20polynomial%20equations%20in%20traditional%20China(Lam%20Lay%20Yong).pdf #HornersMethod #NumericalAnalysis