1. Consider the system of algebraic equations Xị + x22 – 2.5 = 0 X1 X2 +3x12 – 3.1 = 0 The Newton-Raphson (NR) method is to be used to solve it with initial guess X0,1 X, = Calculate the Jacobian matrix for the above system at any iteration value Xk. What would be a clearly unacceptable value of initial guess xo.1? (Fully justify this answer) a Calculate the inverse of the Jacobian matrix at any iteration value x. Using xo,1 = 1, perform by hand one iteration of the NR algorithm. b

1. Consider the system of algebraic equations Xị + x22 – 2.5 = 0 X1 X2 +3x12 – 3.1 = 0 The Newton-Raphson (NR) method is to be used to solve it with initial guess X0,1 X, = Calculate the Jacobian matrix for the above system at any iteration value Xk. What would be a clearly unacceptable value of initial guess xo.1? (Fully justify this answer) a Calculate the inverse of the Jacobian matrix at any iteration value x. Using xo,1 = 1, perform by hand one iteration of the NR algorithm. b

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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Question

1.
Consider the system of algebraic equations
Xị + x22 – 2.5 = 0
X1 X2 +3x12 – 3.1 = 0
The Newton-Raphson (NR) method is to be used to solve it with initial
guess
X0,1
X, =
Calculate the Jacobian matrix for the above system at any iteration value Xk.
What would be a clearly unacceptable value of initial guess xo.1? (Fully justify
this answer)
a
Calculate the inverse of the Jacobian matrix at any iteration value x. Using xo,1
= 1, perform by hand one iteration of the NR algorithm.
b

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