Consider Ar = b where A = [0.780 0.563] 0.913 0.659 b= [0.217 [0.254] T The exact solution is a = [1 -1]. Suppose the two approximate solutions are a = [0.999 -1.001] and a= [0.341 -0.087] ¹. (a) Find and compare the forward errors of xa and x. Use infinity norm. (b) Find and compare the backward errors of xa and ab. Use infinity norm.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 1E
Question
Consider Ar = b where
[0.780 0.563] [0.217]
A =
b=
0.913 0.659 0.257
The exact solution is x = [1 −1]¹. Suppose the two approximate solutions are ca = [0.999 -1.001]
and a= [0.341 -0.087] ¹.
(a) Find and compare the forward errors of xa and xb. Use infinity norm.
(b) Find and compare the backward errors of ra and xb. Use infinity norm.
Transcribed Image Text:Consider Ar = b where [0.780 0.563] [0.217] A = b= 0.913 0.659 0.257 The exact solution is x = [1 −1]¹. Suppose the two approximate solutions are ca = [0.999 -1.001] and a= [0.341 -0.087] ¹. (a) Find and compare the forward errors of xa and xb. Use infinity norm. (b) Find and compare the backward errors of ra and xb. Use infinity norm.
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