Maybe video about how to write code for polynomial equation solver 1. Eigenvalues method (QR method with shifts and deflation) 2. Bairstow method (deflation with quadratic factor, in my opinion Newton's method which is used in this algorithm causes the problems) 3. Jenkins - Traub (RPOLY version)
x^3 grows faster than x^2+3x+3, so there is a real root between 2 and 3, somewhat closer to 3 than 2. Fixed-point iteration x←∛(x^2+3x+3) starting with x=2.6 gives x=2.59867... What about the other two roots? Divide x^3-x^2-3x-3=0 by (x-2.59867...): x^2+1.59867x+1.15444=0 yields x=(-1.59867±i1.43579)/2=-0.79934...±i0.71799...
Maybe video about how to write code for polynomial equation solver
1. Eigenvalues method (QR method with shifts and deflation)
2. Bairstow method (deflation with quadratic factor, in my opinion Newton's method which is used in this algorithm causes the problems)
3. Jenkins - Traub (RPOLY version)
The last bit was so flawless 😂
Such fun! 💪
Nice,completing the cube😊
x^3 grows faster than x^2+3x+3, so there is a real root between 2 and 3, somewhat closer to 3 than 2. Fixed-point iteration x←∛(x^2+3x+3) starting with x=2.6 gives x=2.59867...
What about the other two roots? Divide x^3-x^2-3x-3=0 by (x-2.59867...): x^2+1.59867x+1.15444=0 yields x=(-1.59867±i1.43579)/2=-0.79934...±i0.71799...
Nice!
Very nice!
I found Method 1; but failed in finding Method 2 because I missed the initial multiplication through by 9.
👍
Any time I'm solving a cubic equation i will break it down in terms of (x + something else)
method 2 was good