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Now let us experiment with the sequence {ek}keN C R+ given by ek+1 = aek, k = 0, 1, 2, ... (*) for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R2. What does the slope of this line tell us?

Now let us experiment with the sequence {ek}keN C R+ given by ek+1 = aek, k = 0, 1, 2, ... (*) for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R2. What does the slope of this line tell us?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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Now let us experiment with the sequence {ek}kEN C R+ given by ek+1=aek, k = 0, 1, 2, ... for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R². What does the slope of this line tell us?
Transcribed Image Text:Now let us experiment with the sequence {ek}kEN C R+ given by ek+1=aek, k = 0, 1, 2, ... for fixed constants a > 0 and p > 0, which models the errors of a numerical method with order of convergence p. d) Apply the logarithm to both sides of the recursion (*). Use the rules for logarithms to deduce that all pairs (log(ek), log(ek+1)) are located on a straight line in R². What does the slope of this line tell us?
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