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Apply two iterations of the Secant Steepest Accent Method the find the optimum. f(x)=x²-27 x + 12 + y² Starting with the initial points (2,2) Appendix: Secant Steepest Accent Steepest Ascent Method Algorithm a) Start from initial point (xo.Yo) ar ar b) Calculate the gradient ax'ay (Best direction) c) Calculate g(h), a function of a vector along the gradient direction af af g(h) = f(xo+h.yo+ 5/ h) ду g(h) is a 1-D function of h generated from the 2-D function of and y d) Calculate g'(h) to find h' that have the maximum along g(h) e) Transfer h' back to (x₁.₁) af (X1,Y₁)=(xo + h.yo+h) af ax ду

Apply two iterations of the Secant Steepest Accent Method the find the optimum. f(x)=x²-27 x + 12 + y² Starting with the initial points (2,2) Appendix: Secant Steepest Accent Steepest Ascent Method Algorithm a) Start from initial point (xo.Yo) ar ar b) Calculate the gradient ax'ay (Best direction) c) Calculate g(h), a function of a vector along the gradient direction af af g(h) = f(xo+h.yo+ 5/ h) ду g(h) is a 1-D function of h generated from the 2-D function of and y d) Calculate g'(h) to find h' that have the maximum along g(h) e) Transfer h' back to (x₁.₁) af (X1,Y₁)=(xo + h.yo+h) af ax ду

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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Apply two iterations of the Secant Steepest Accent Method the find the optimum. f(x)=x²-27 x + 12 + y² Starting with the initial points (2,2) Appendix: Secant Steepest Accent Steepest Ascent Method Algorithm a) Start from initial point (xo.Yo) b) Calculate the gradient(Best direction) c) Calculate g(h), a function of a vector along the gradient direction af g(h) = f(xo +/h.yo+h) g(h) is a 1-D function of h generated from the 2-D function of and y d) Calculate g' (h) to find h' that have the maximum along g(h) e) Transfer h back to (x₁.₁) af (x₁+₁) = (x₁+=h² h*,yo+h) + dx ду
Transcribed Image Text:Apply two iterations of the Secant Steepest Accent Method the find the optimum. f(x)=x²-27 x + 12 + y² Starting with the initial points (2,2) Appendix: Secant Steepest Accent Steepest Ascent Method Algorithm a) Start from initial point (xo.Yo) b) Calculate the gradient(Best direction) c) Calculate g(h), a function of a vector along the gradient direction af g(h) = f(xo +/h.yo+h) g(h) is a 1-D function of h generated from the 2-D function of and y d) Calculate g' (h) to find h' that have the maximum along g(h) e) Transfer h back to (x₁.₁) af (x₁+₁) = (x₁+=h² h*,yo+h) + dx ду
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