1. (a) Consider the polynomial (x − 1)(x − 2) = x² -3x+2 which has exact roots x = 1 and x = 2. Suppose some numerical algorithm finds approximate roots equal to ✰ = 1.1 and = 1.9. For each root determine the forward error and the relative forward error. Then, for each approximate root, find a perturbed quadratic, that is as close to the original quadratic as possible, such that the approximate root to the original quadratic is the exact root to the perturbed quadratic. For each approximate root, what is the backward error and what is the relative backward error? (b) For each approximate root, draw a diagram like the ones we've seen in the course notes, showing the relationship between the original problem the perturbed problem, the exact root, and the approximate root. Make sure to include the value of the forward error and the backward error in the diagram.

1. (a) Consider the polynomial (x − 1)(x − 2) = x² -3x+2 which has exact roots x = 1 and x = 2. Suppose some numerical algorithm finds approximate roots equal to ✰ = 1.1 and = 1.9. For each root determine the forward error and the relative forward error. Then, for each approximate root, find a perturbed quadratic, that is as close to the original quadratic as possible, such that the approximate root to the original quadratic is the exact root to the perturbed quadratic. For each approximate root, what is the backward error and what is the relative backward error? (b) For each approximate root, draw a diagram like the ones we've seen in the course notes, showing the relationship between the original problem the perturbed problem, the exact root, and the approximate root. Make sure to include the value of the forward error and the backward error in the diagram.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section11.11: Separable Programming

Problem 2P

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