Bardbl x bardbl lessorequalslant k a bardbl r bardbl

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bardbl x bardbl lessorequalslant K ( A ) bardbl r bardbl bardbl b bardbl Rule of Thumb: When applying GE+PP, you lose approxi- mately log 10 K ( A ) decimal digits of accuracy due to magni- fication of rounding errors. Why? Suppose K ( A ) = 10 10 (common): Even in the best possible case, bardbl r bardbl bardbl b bardbl 2 × 10 16 ( ǫ M ) Relative error in x is lessorequalslant 10 10 · 2 × 10 16 10 6 . Losing 10 digits of accuracy makes even tiny errors sig- nificant! Example from previous slide: K ( A ) = 201 . Then log 10 (201) 2 . 3 and so only 2 digits are lost. No worries! Still have 14 correct digits in double precision. October 3, 2018 c circlecopyrt John Stockie (SFU)
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