Method of Steepest Descent -- from Wolfram MathWorld

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also called the gradient descent method, starts at a point P_0 and, as many times as needed, moves from P_i to P_(i+1) by minimizing along the line extending from P_i in the direction of -del f(P_i), the local downhill gradient. When applied to a 1-dimensional function f(x), the method takes the form of iterating

Curves of Steepest Descent for 3D Functions - Wolfram

Schematic plot of banana trees (adapted from Wolfram MathWorld

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Method of Steepest Descent -- from Wolfram MathWorld

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Steepest Descent Method - an overview