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Big Loss of Precision
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From: |
Thomas D. Dean |
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Subject: |
Big Loss of Precision |
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Date: |
Sat, 16 Jul 2016 11:35:38 -0700 |
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User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.8.0 |
The cross product of two vectors is orthogonal to both. The dot product
of two orthogonal vectors is zero.
This is not an octave problem, just an ill-formed situation.
octave:1405> printf(" %.20f\n",V);
3.99120302628332668249
-0.91842329903575536942
1.29246846883179156151
octave:1406> printf(" %.20f\n",R);
-1518.35794621729837672319
-4017.17627231122196462820
4816.75939627815478161210
octave:1407> dot(cross(R,V),R)
ans = 1.4901e-08
octave:1408> dot(cross(R,V),V)
ans = 3.6380e-12
cross has 6 multiplications and 3 add/subtract
dot has 3 multiplications and 3 add/subtract
Octave eps is 2.2204e-16
machine eps is 1.11022e-16 (quadmath 1.925930e-34).
This case has a very serious loss of precision!
Tom Dean
- Big Loss of Precision,
Thomas D. Dean <=