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