Let A be a 10 × 10 matrix with cond∞(A) = 5×106.Suppose that the solution of a system Ax = b is computedin 15-digit decimal arithmetic and the relativeresidual, ||r||∞/||b||∞, turns out to be approximatelytwice the machine epsilon. How many digits of accuracywould you expect to have in your computedsolution? Explain.
Let A be a 10 × 10 matrix with cond∞(A) = 5×106.Suppose that the solution of a system Ax = b is computedin 15-digit decimal arithmetic and the relativeresidual, ||r||∞/||b||∞, turns out to be approximatelytwice the machine epsilon. How many digits of accuracywould you expect to have in your computedsolution? Explain.
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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Let A be a 10 × 10 matrix with cond∞(A) = 5×106.
Suppose that the solution of a system Ax = b is computed
in 15-digit decimal arithmetic and the relative
residual,
||r||∞/||b||∞, turns out to be approximately
twice the machine epsilon. How many digits of accuracy
would you expect to have in your computed
solution? Explain.
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