Cubic Splines @OscarVeliz

Oscar Veliz | Cubic Splines @OscarVeliz | Uploaded 13 years ago | Updated 2 hours ago
Function approximation using Cubic Splines and Natural Cubic Splines including discussion about figuring out if two sets of equations are splines. Important note: around 1:10 the functions also need to go through the points at the ends
ax1^3 + bx1^2 + cx1 + d = y1
ex3^3 + fx3^2 + gx3 + h = y3
A video covering this correction can be found here youtu.be/4jw0cjddmB8

Chapters
0:00 Intro
0:05 Ways to Approximate a Function
0:23 Splines
1:06 Calculating Cubic Splines
1:40 Example 1
2:26 Example 2
3:24 Thanks For Watching

Further Viewing:
Lagrange Polynomials youtu.be/GtJKUIG9KXI

#CubicSpline #NumericalAnalysis

$Bairstows Method Bairstows Method for finding the roots of polynomials including complex roots. Discussion of method derivation, relation to synthetic division of two variables, stopping condition, selection of initial values, fractals, and historical context. Submission for Summer of Math Exposition 2 contest by @3blue1brown. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:36 Factoring with monomial 01:13 Factoring with quadratic 01:40 Synthetic Division 1 variable 02:16 Synthetic Division 2 variables 03:22 Solving for roots 03:50 Different u and v 04:24 Describing Notation 05:22 Solving Nonlinear System 07:01 Another Synthetic Division 07:45 Updating u & v 08:27 Bairstow Iteration Example 08:56 Bairstow Iteration Example 2 09:22 Note on Quadratic Equation 09:42 Bairstow Full Algorithm 10:51 Complex Roots Example 11:33 Bairstow Fractals 12:23 Picking u & v 12:46 Henrici Starting Values 13:08 Bairstows Original Problem 14:40 Oscars Notes 15:24 Outro Recommended Viewing: Horners Method https://youtu.be/zEvfkSuPqWk Graeffes Method https://youtu.be/92oh5gYUP7Y Generalized Newtons Method https://youtu.be/p0SBubUfwiI Reference links: Applied Aerodynamics by Bairstow https://books.google.com/books?id=GIUQAQAAMAAJ Elements of Numerical Analysis by Henrici https://archive.org/details/elements-of-numerical-analysis-by-peter-henrici A Modified Bairstow Method for Multiple Zeros of a Polynomial by F. M. Carrano https://doi.org/10.1090/S0025-5718-1973-0334492-5 Background music Drifting at 432 Hz by @UnicornHeads #SoME2 #NumericalAnalysis #BairstowsMethod$

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