Taylor Series/Newton Raphson Method question -Link Fixed

  • Context: Undergrad 
  • Thread starter Thread starter Shadow_7
  • Start date Start date
  • Tags Tags
    Method Taylor
Click For Summary
SUMMARY

The discussion focuses on the application of the Newton Raphson Method in conjunction with the concepts of the x^* symbol and the "argmin" function. The x^* symbol denotes the optimal solution, while "argmin" refers to the argument that yields the minimum value of a function. Participants clarify that when using the Newton Raphson Method, one should return the coordinates (e.g., (1,3)) that produce the minimum value rather than the minimum value itself. This distinction is crucial for correctly interpreting results in optimization problems.

PREREQUISITES
  • Understanding of the Newton Raphson Method for root finding
  • Familiarity with optimization concepts, specifically "argmin" and "min"
  • Basic knowledge of mathematical notation, including symbols like x^*
  • Experience with function minimization techniques
NEXT STEPS
  • Study the mathematical foundations of the Newton Raphson Method
  • Learn about optimization techniques, focusing on "argmin" and its applications
  • Explore examples of function minimization in calculus
  • Review complex conjugates and their relevance in optimization contexts
USEFUL FOR

Students and professionals in mathematics, engineering, and data science who are working with optimization problems and require a deeper understanding of the Newton Raphson Method and related concepts.

Shadow_7
Messages
5
Reaction score
0
http://uploadpic.org/storage/2011/dGTvcFGgvl4VYoVB40HpLSMxH.jpeg

Can somebody guide me through this? I know how to apply Newton Raphson Method, but the x^* symbol and "argmin" function are kinda new to me. I am re referring to part (c). Thanks.
 
Physics news on Phys.org
The asterisk usually refers to the optimal solution (it can also indicate a complex conjugate, but this is not the case :) ).
"min" refers to the minimum of..., ie "Give me the minimal value of this function".

"arg" tells you "You calculated the minimum, right? so don't give me the minimal value, but rather give me the argument that yields the minimum". So if you minimize the given function f() and you get a value of f(1,3)=4, for example, you need to return (1,3) and not 4. This also relates to the fact the the left hand side has x* so obviously you need to put there the X coordinates and not the minimal value of the function.
 

Similar threads

Undergrad Taylor Series/Newton Raphson Method question
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Newton-Raphson Method With Complex Numbers
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Regarding Error Bound of Taylor Series
  • · Replies 8 ·
Replies
8
Views
3K
Calculate tilt angle of a bar lifted via two ropes on fixed points
  • · Replies 7 ·
Replies
7
Views
3K
How Can Newton-Raphson Method Solve These Complex Nonlinear Equations?
  • · Replies 6 ·
Replies
6
Views
3K
MHB How to Solve Non-Linear Equations of 3 Variables Using Newton-Raphson Method?
  • · Replies 1 ·
Replies
1
Views
4K
Newton-Raphson Method for Non-linear System of 3 variables in Matlab
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad The algorithms involved in finding a solution with numerical methods
  • · Replies 14 ·
Replies
14
Views
3K
Newton Raphson Method for Finding Roots: Bessel's Function J0(x) near x=5
  • · Replies 1 ·
Replies
1
Views
2K