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## Accuracy and Stability of Numerical Algorithms, Second Edition | Engineering

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NM8 3 Stability of Numerical Solutions

Higham 1. Floating point numbers are not equally spaced. Common error not to normalize errors and residuals. Default: round to nearest, round to even in case of tie. A NaN compares as unordered with everything. Transcendental functions may not provide full accuracy. Square root, division may be software only.

No standards. Most of the same issues see below apply. Cancellation Cancellation brings earlier errors into prominence but is not always a bad thing.

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Numbers being subtracted may be error free. Cancellation may be a symptom of intrinsic ill conditioning of problem. Inaccurate for needle-shaped triangles, e. Gives an accurate answer for all data. Lack of guard digit is dangerous. Rounding may be biased.

## Accuracy and Stability of Numerical Algorithms

Fused Multiply-Add Instruction cont. Three Misconceptions of Floating Point Arithmetic An Innocuous Calculation? Myth 2Increasing the precision at which a computation isperformed increases the accuracy of the answer. Cray and NEC machines both implemented complex division in this way.

This resulted in an Operand Error. Use extended precision internally: a precision at least 1.

## ISBN 13: 9780898715217

Input and output arguments remain single or double. Reference implementation employs the double-double format, giving an extended precision of about bits.