Floating-point operations In general, real numbers (with infinite decimal expansions) cannot be represented exactly in a computer by floating-point numbers (with finite decimal expansions). Suppose that floating-point numbers on a particular computer carry an error of at most 10 –16 . Estimate the maximum error that is committed in doing the following arithmetic operations. Express the error in absolute and relative (percent) terms. a. f ( x , y ) = xy b. f ( x , y ) = x / y c. F ( x , y , z ) = xz d. F ( x , y , z ) = ( x / y ) / z
Floating-point operations In general, real numbers (with infinite decimal expansions) cannot be represented exactly in a computer by floating-point numbers (with finite decimal expansions). Suppose that floating-point numbers on a particular computer carry an error of at most 10 –16 . Estimate the maximum error that is committed in doing the following arithmetic operations. Express the error in absolute and relative (percent) terms. a. f ( x , y ) = xy b. f ( x , y ) = x / y c. F ( x , y , z ) = xz d. F ( x , y , z ) = ( x / y ) / z
Solution Summary: The author calculates the maximum error for f(x,y)=xy and expresses it in absolute and relative terms.
Floating-point operations In general, real numbers (with infinite decimal expansions) cannot be represented exactly in a computer by floating-point numbers (with finite decimal expansions). Suppose that floating-point numbers on a particular computer carry an error of at most 10–16. Estimate the maximum error that is committed in doing the following arithmetic operations. Express the error in absolute and relative (percent) terms.
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