Oscar Veliz | Horner's Method @OscarVeliz | Uploaded 6 years ago | Updated 1 hour ago
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 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 youtu.be/E24zUEKqgwQ
Laguerre's Method youtu.be/blOARV4lnIM
Newton Fractals youtu.be/MWD2A0Vg2V0
Durand-Kerner Method youtu.be/5JcpOj2KtWc
Aberth-Ehrlich Method youtu.be/XIzCzfMDSzk
Bairstow's Method youtu.be/iUGEk6kngFw
References:
Horner's paper jstor.org/stable/107508
Ruffini doi.org/10.1090/S0002-9904-1911-02072-9
Chemla's paper 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 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
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 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 youtu.be/E24zUEKqgwQ
Laguerre's Method youtu.be/blOARV4lnIM
Newton Fractals youtu.be/MWD2A0Vg2V0
Durand-Kerner Method youtu.be/5JcpOj2KtWc
Aberth-Ehrlich Method youtu.be/XIzCzfMDSzk
Bairstow's Method youtu.be/iUGEk6kngFw
References:
Horner's paper jstor.org/stable/107508
Ruffini doi.org/10.1090/S0002-9904-1911-02072-9
Chemla's paper 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 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
