Timeline for Is order of matrix multiplication affecting numerical accuracy of the result?
Current License: CC BY-SA 4.0
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| Jul 12, 2019 at 10:49 | comment | added | Simon | You could also use a system with arbitrary precision (given sufficient memory), instead of a system with greater precision. I have Mathematica in mind. | |
| Jul 9, 2019 at 13:00 | comment | added | Gerardo Zinno | @abukaj I'm not sure, but I think there isn't a way to tell a priori which way is gonna be more precise since it depends on which numbers are in the matrix. The only thing you could in theory do is multiply the matrices by hand or on a system with greater precision and then compare the result to see which way was better. But then again, with different matrices the you would have to repeat it all again. Also, you would die before you could multiply by hand those matrices. | |
| Jul 9, 2019 at 11:33 | comment | added | abukaj | But is there any rule in which order the matrix multiplication should be performed for maximum accuracy? I can prove that for matrices which all elements have the same sign the error estimate is not affected by the order of multiplication. I have no idea whether that holds for any matrices (due to the possible loss of significant digits). | |
| Jul 8, 2019 at 23:27 | history | edited | Gerardo Zinno | CC BY-SA 4.0 |
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| Jul 8, 2019 at 22:46 | history | edited | Gerardo Zinno | CC BY-SA 4.0 |
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| Jul 8, 2019 at 22:37 | history | edited | Gerardo Zinno | CC BY-SA 4.0 |
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| Jul 8, 2019 at 19:36 | comment | added | user888379 | For additional details: "What every computer scientist should know about floating-point arithmetic". The upshot is that getting floating-point arithmetic right is challenging, as Gerardo Zinno's answer illustrates. | |
| Jul 8, 2019 at 18:38 | history | edited | Gerardo Zinno | CC BY-SA 4.0 |
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| Jul 8, 2019 at 18:25 | history | edited | Gerardo Zinno | CC BY-SA 4.0 |
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| Jul 8, 2019 at 18:25 | review | First posts | |||
| Jul 8, 2019 at 21:10 | |||||
| Jul 8, 2019 at 18:20 | history | answered | Gerardo Zinno | CC BY-SA 4.0 |