If x and y are floating-point numbers, then the evaluation off(x, y)- Væ²= -x – Vx – yin a floating point system may be very inaccurate due to cancellation. To illustrate, use baseb = 10, precision k = 4, idealized, chopping floating-point arithmetic below. (a) Let x =and determine the relative error.-123.4 = -0.1234 × 103 and y1.234 = 0.1234 x 10', evaluate fl(f(x,y))(b) Determine a different way to evaluate f (x, y) which does not suffer from subtractivecancellation.(c) Repeat part (a) using the new form of f(x, y) that you derived in (b) to show that itdoes not suffer from subtractive cancellation for the given values.

Given:- If x and y are floating point number then the evaluation is:…

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 & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 90E

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Question

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.

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