3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point system, this expression is subject to a large increase of its relative error (catastrophic cancelation) when x is a very small number. b. Find a formula that is equivalent to the one above in exact mathematics and that does not suffer of catastrophic cancelation.
3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point system, this expression is subject to a large increase of its relative error (catastrophic cancelation) when x is a very small number. b. Find a formula that is equivalent to the one above in exact mathematics and that does not suffer of catastrophic cancelation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3. Consider the function f(x) = r - :
1+x
1-x
a. Explain why, when evaluated in a floating
point system, this expression is subject to
a large increase of its relative error
(catastrophic cancelation) when x is a
very small number.
b. Find a formula that is equivalent to the
one above in exact mathematics and that
does not suffer of catastrophic
cancelation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f8e76e9-b615-4c21-9322-95ee6ed50807%2Ffb710940-6854-4a9a-bdfe-d54b5867b4ee%2F7gojdxh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the function f(x) = r - :
1+x
1-x
a. Explain why, when evaluated in a floating
point system, this expression is subject to
a large increase of its relative error
(catastrophic cancelation) when x is a
very small number.
b. Find a formula that is equivalent to the
one above in exact mathematics and that
does not suffer of catastrophic
cancelation.
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