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Compare the gradients of the function f(X) = 100(x2 – x})² + (1 – x1)? at X = {0} given by the following methods: (a) Analytical differentiation (b) Central difference method (c) Forward difference method (d) Backward difference method Use a perturbation of 0.005 for x1 and x2 in the finite-difference methods.

Compare the gradients of the function f(X) = 100(x2 – x})² + (1 – x1)? at X = {0} given by the following methods: (a) Analytical differentiation (b) Central difference method (c) Forward difference method (d) Backward difference method Use a perturbation of 0.005 for x1 and x2 in the finite-difference methods.

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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6.33 Compare the gradients of the function f (X) = 100(x2 – x})² + (1 – x1)² at X = {0} given by the following methods: (0.51 (a) Analytical differentiation (b) Central difference method (c) Forward difference method (d) Backward difference method Use a perturbation of 0.005 for x1 and x2 in the finite-difference methods.
Transcribed Image Text:6.33 Compare the gradients of the function f (X) = 100(x2 – x})² + (1 – x1)² at X = {0} given by the following methods: (0.51 (a) Analytical differentiation (b) Central difference method (c) Forward difference method (d) Backward difference method Use a perturbation of 0.005 for x1 and x2 in the finite-difference methods.
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