Convergence Properties of Newton’s Method
Newton’s method converges quadratically, meaning that with each iteration, the number of digits approximately doubles. Its convergence may be affected by several factors:
- Choice of Initial Guess: The convergence of Newton’s method can depend significantly on the initial guess. If the initial guess is close to the minimum, it usually converges rapidly. However, far-off initial guesses may lead to slow convergence or even divergence.
- Behavior of the Function: Newton’s method assumes that the function is well-behaved in the vicinity of the minimum, meaning it’s smooth and has continuous first and second derivatives. Discontinuities, singularities, or regions where derivatives are difficult to compute can affect convergence.
- Convergence Criteria: Newton’s method typically terminates when the change in x between iterations becomes small enough, or when the function value becomes close to zero.
Newton’s method in Machine Learning
Optimization algorithms are essential tools across various fields, ranging from engineering and computer science to economics and physics. Among these algorithms, Newton’s method holds a significant place due to its efficiency and effectiveness in finding the roots of equations and optimizing functions, here in this article we will study more about Newton’s method and it’s use in machine learning.
Table of Content
- Newton’s Method for Optimization
- Second-Order Approximation
- Newton’s Method for Finding Local Minima or Maxima in Python
- Convergence Properties of Newton’s Method
- Complexity of Newton’s Method
- Time Complexity of Newton’s Method
- Parameter Estimation in Logistic Regression using Newton’s Method
- Data Fitting with Newton’s Method
- Newton’s Method vs Other Optimization Algorithms
- Applications of Newton’s Method
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