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If x and y are floating-point numbers, then the evaluation of f(x, y) : = -x – Vr2 - Y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic below.

If x and y are floating-point numbers, then the evaluation of f(x, y) : = -x – Vr2 - Y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic below.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.1: Exponents
Problem 5E
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If x and y are floating-point numbers, then the evaluation of f(x, y) - Væ² = -x – Vx – y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic below.
Transcribed Image Text:If x and y are floating-point numbers, then the evaluation of f(x, y) - Væ² = -x – Vx – y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic below.
(a) Let x = and determine the relative error. -123.4 = -0.1234 × 103 and y 1.234 = 0.1234 x 10', evaluate fl(f(x,y)) (b) Determine a different way to evaluate f (x, y) which does not suffer from subtractive cancellation. (c) Repeat part (a) using the new form of f(x, y) that you derived in (b) to show that it does not suffer from subtractive cancellation for the given values.
Transcribed Image Text:(a) Let x = and determine the relative error. -123.4 = -0.1234 × 103 and y 1.234 = 0.1234 x 10', evaluate fl(f(x,y)) (b) Determine a different way to evaluate f (x, y) which does not suffer from subtractive cancellation. (c) Repeat part (a) using the new form of f(x, y) that you derived in (b) to show that it does not suffer from subtractive cancellation for the given values.
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