(b) Consider the function F : R³→R³ such that 2x1 2x2 cos x3 – e²2r –x3 sin x3 – 2e"2 X3 +4 F(x) = (i) Derive the Jacobian of F. (ii) Write down the linear model Mr(x) as a function of x1, x2 and x3 at the point ak = (0, 1, 0)". (You may use the quantity e without substituting its numerical value.) Compute xk+1; the zero of Mr(x). (iii) Compute the Newton direction at x = (0, 1, 0)".
(b) Consider the function F : R³→R³ such that 2x1 2x2 cos x3 – e²2r –x3 sin x3 – 2e"2 X3 +4 F(x) = (i) Derive the Jacobian of F. (ii) Write down the linear model Mr(x) as a function of x1, x2 and x3 at the point ak = (0, 1, 0)". (You may use the quantity e without substituting its numerical value.) Compute xk+1; the zero of Mr(x). (iii) Compute the Newton direction at x = (0, 1, 0)".
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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Consider the function F : R3.→ R³ such that
2x1
2x2 cos a3 – e#2 x
-až sin r3 – 2e"2 x3 + 4,
F(x) =
(i) Derive the Jacobian of F.
(ii) Write down the linear model Mr(x) as a function of x1, x2 and æ3 at the point
Tk = (0, 1, 0)". (You may use the quantity e without substituting its numerical
value.) Compute xk+1, the zero of Mr(x).
(iii) Compute the Newton direction at a = (0, 1, 0)".
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