wishfulthinking said:I am not understanding how to use the method of steepest descent aka the saddle point method. Any help would be appreciated, especially step-by-step explanation!
Well, how familiar are you with using root finding algorithms on single variable equations, like finding the roots of polynomials?wishfulthinking said:Thanks, I did Google the method, but I'm still not quite sure how to use it.
wishfulthinking said:Thanks for taking the time out to reply. Specifically, I'm being asked to approximate an integral using the method. I've never learned this before and it's not in our textbook. My teacher said to look for outside resources, I'm just not understanding it and was hoping someone could explain it to me.
The method of steepest descent is an optimization technique used to find the minimum of a multivariable function. It is also known as the gradient descent method or the steepest descent algorithm.
The method of steepest descent works by iteratively moving in the direction of the steepest descent, or the direction of the negative gradient, of the function at a given point. This process continues until a minimum point is reached.
The method of steepest descent is commonly used in machine learning and optimization problems where the goal is to find the minimum of a cost function. It is also used in physics and engineering to solve various problems.
The method of steepest descent is relatively easy to implement and can be applied to a wide range of problems. It also converges quickly to a local minimum and does not require the calculation of second derivatives.
The method of steepest descent may not always find the global minimum and can get stuck in local minima. It also requires careful selection of the learning rate to ensure convergence. Additionally, it may take a large number of iterations to reach the minimum for highly non-convex functions.