Using Newton Raphson for Root Finding and Parameters' Estimation

In summary, the Newton Raphson method is an iterative algorithm used for root finding in numerical analysis and optimization problems. It works by using the derivative of a function to refine an initial guess for the root until a satisfactory approximation is obtained. The method is known for its speed, accuracy, and ability to handle complex functions and multiple roots. However, it may fail if the initial guess is not close enough to the root and requires knowledge of the function's derivative. It can also be used for parameter estimation in regression analysis and curve fitting.
  • #1
adeeyo
20
0
Goood Day,

I have a cubic root equation. I use Newton-raphson for finding the roots. I want to do parameter estimation (tuning of the equation parameters to be able to give better prediction) using experiment data. Can anyone help me on how to do this?

Thanks for your anticipated help
Regards,
Isa
 
Physics news on Phys.org
  • #2
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 

1. What is Newton Raphson method and how is it used for root finding?

The Newton Raphson method is an iterative algorithm used to find the roots of a mathematical function. It works by making an initial guess for the root, then using the derivative of the function to refine the guess until a satisfactory approximation of the root is obtained. This method is commonly used in numerical analysis and optimization problems.

2. How does the Newton Raphson method work?

The Newton Raphson method works by using the derivative of a function to approximate the root of the function. It starts with an initial guess for the root, then uses the derivative of the function to calculate a better guess. This process is repeated until the desired level of accuracy is achieved.

3. What are the advantages of using Newton Raphson method?

One of the main advantages of using the Newton Raphson method is its speed and efficiency in finding the roots of a function. It also provides a high degree of accuracy, making it a popular choice for root finding and parameter estimation in scientific and engineering applications. Additionally, it can handle complex functions and multiple roots.

4. What are the limitations of Newton Raphson method?

One of the limitations of the Newton Raphson method is that it may fail if the initial guess is not close enough to the root. It also requires knowledge of the derivative of the function, which may not be readily available for all functions. Additionally, for functions with multiple roots, the method may converge to a different root than the one desired.

5. How is Newton Raphson method used for parameters' estimation?

The Newton Raphson method can be used for parameters' estimation by treating the parameters as the variables in the function and finding their values that make the function equal to the observed data. By iterating through the method, the parameters can be refined until they provide the best fit for the data. This approach is commonly used in regression analysis and curve fitting.

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