Tag Archives: error_analysis

How and How Not to Compute a Relative Error

The relative error in a scalar as an approximation to a scalar is the absolute value of . I recently came across a program in which had been computed as . It had never occurred to me to compute it … Continue reading

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The Rise of Mixed Precision Arithmetic

For the last 30 years, most floating point calculations in scientific computing have been carried out in 64-bit IEEE double precision arithmetic, which provides the elementary operations of addition, subtraction, multiplication, and division at a relative accuracy of about . … Continue reading

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Tiny Relative Errors

Let and be distinct floating point numbers. How small can the relative difference between and be? For IEEE double precision arithmetic the answer is , which is called the unit roundoff. What if we now let and be vectors and … Continue reading

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