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)...

3. Consider the function f(x) = r - :<br>1+x<br>1-x<br>a. Explain why, when evaluated in a floating<br>point system, this expression is subject to<br>a large increase of its relative error<br>(catastrophic cancelation) when x is a<br>very small number.<br>b. Find a formula that is equivalent to the<br>one above in exact mathematics and that<br>does not suffer of catastrophic<br>cancelation.<br>

Extracted 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.

Jun 04, 2022

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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)...

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