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Perform the tasks below for the problem: f(x) = 2ỉ +9x2, with the initial point (#1, #2)= (5, 1) (a) Sketch a few contours of constant value of the function on graph paper. (b) Derive an expression for the optimal step size B' for the arbitrary initial point x'. (c) Go through three iterations of the method of steepest descent starting from (5, 1) and plot the results.

Perform the tasks below for the problem: f(x) = 2ỉ +9x2, with the initial point (#1, #2)= (5, 1) (a) Sketch a few contours of constant value of the function on graph paper. (b) Derive an expression for the optimal step size B' for the arbitrary initial point x'. (c) Go through three iterations of the method of steepest descent starting from (5, 1) and plot the results.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4.4.2 Perform the tasks below for the problem: f(x) = 2i + 922, with the initial point (x, x2) = (5, 1) (a) Sketch a few contours of constant value of the function on graph paper. (b) Derive an expression for the optimał step size 6* for the arbitrary initial point x'. (c) Go through three iterations of the method of steepest descent starting from (5, 1) and plot the results. Handwritten solution only
Transcribed Image Text:4.4.2 Perform the tasks below for the problem: f(x) = 2i + 922, with the initial point (x, x2) = (5, 1) (a) Sketch a few contours of constant value of the function on graph paper. (b) Derive an expression for the optimał step size 6* for the arbitrary initial point x'. (c) Go through three iterations of the method of steepest descent starting from (5, 1) and plot the results. Handwritten solution only
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