7. If the bisection method is used starting with the interval [2, 3], how many steps must betaken to compute a root with absolute accuracy < 10-6? Answer the same question forthe relative accuracy. What about to full single precision on the Marc-32 in each case?

Answered: -If the bisection method is used…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Expert Solution

Step 1: Apply the definition of bisection method.

Let $open square brackets a subscript 0 comma b subscript 0 close square brackets$ be the initial interval of the bisection method.

Use the following formulae, to obtain the solution.

Absolute error with accuracy $epsilon$ is given by the formula $fraction numerator b subscript 0 minus a subscript 0 over denominator 2 to the power of n end fraction less or equal than epsilon$ .
Relative error with accuracy $epsilon$ is given by the formula $1 over 2 to the power of n plus 1 end exponent open vertical bar fraction numerator b subscript 0 minus a subscript 0 over denominator a subscript 0 end fraction close vertical bar less or equal than epsilon$ .