This problem is from the textbook Numerical analysis : mathematics of scientific computing 3rd edition. It is from chapter 2 section 3. I just want the answer to 9. I understand most of the question. I just mainly want to know how to calculate the stability of the algorithm. 8. The Fibonacci sequence is generated by the formulasTo=1n=1rn+1 =rn+rn-1The sequence therefore starts out 1, 1, 2, 3, 5, 8, 13, 21, 34,.... Prove that the sequence[2rn/r-1] converges to 1 + √5. Is the convergence linear, superlinear, quadratic?9. (Continuation) If the recurrence relation in the preceding problem is used with startingvalues ro = 1 and r₁ = (1-√√5)/2, what is the theoretically correct value of r, (n ≥ 2)?Can the recurrence relation provide a stable means for computing r, in this case?

Given that:To find: The theoretical correct value of .Can the recurrence relation provide a stable…

(Continuation) If the recurrence relation in the preceding problem is used with starting values ro = 1 and r₁ = (1-√5)/2, what is the theoretically correct value of r, (n ≥ 2)? Can the recurrence relation provide a stable means for computing r, in this case?

(Continuation) If the recurrence relation in the preceding problem is used with starting values ro = 1 and r₁ = (1-√5)/2, what is the theoretically correct value of r, (n ≥ 2)? Can the recurrence relation provide a stable means for computing r, in this case?

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

This problem is from the textbook Numerical analysis : mathematics of scientific computing 3rd edition. It is from chapter 2 section 3. I just want the answer to 9. I understand most of the question. I just mainly want to know how to calculate the stability of the algorithm.

8. The Fibonacci sequence is generated by the formulas
To=1
n=1
rn+1 =rn+rn-1
The sequence therefore starts out 1, 1, 2, 3, 5, 8, 13, 21, 34,.... Prove that the sequence
[2rn/r-1] converges to 1 + √5. Is the convergence linear, superlinear, quadratic?
9. (Continuation) If the recurrence relation in the preceding problem is used with starting
values ro = 1 and r₁ = (1-√√5)/2, what is the theoretically correct value of r, (n ≥ 2)?
Can the recurrence relation provide a stable means for computing r, in this case?

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