Eigenvectors
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08-20-2021, 08:21 PM
Post: #9
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RE: Eigenvectors
(12-27-2018 04:32 PM)parisse Wrote: ⋮ Very true! There’s no end to the fun one can have designing and implementing algorithms. As well as considering the (ill- / well-)conditioning of a problem, one can also consider the arithmetics used in implementation (e.g., how round-off or range limits in an employed floating-point arithmetic will interplay with the numerical computations carried out by the algorithm). When I was adding the Sketch feature to the Function Plot view, I had concerns over the use of the already-present floating-point arithmetics when solving 3x3 and 4x4 matrix equations. Since I had a full plate of things to work on, I added higher-precision signed-magnitude arithmetics (1 sign bit + 128 binary digits and 1 sign bit + 160 binary digits, for just a few arithmetic operations) to rule out catastrophic cancellation in sums. (The extended precision arithmetics allowed for absolutely no round-off to be introduced until very near the end of calculation chains, where bounding it was entirely straightforward.) |
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Messages In This Thread |
Eigenvectors - DrD - 12-27-2018, 11:40 AM
RE: Eigenvectors - parisse - 12-27-2018, 12:58 PM
RE: Eigenvectors - DrD - 12-27-2018, 03:58 PM
RE: Eigenvectors - parisse - 12-27-2018, 04:32 PM
RE: Eigenvectors - jte - 08-20-2021 08:21 PM
RE: Eigenvectors - John Keith - 12-27-2018, 04:42 PM
RE: Eigenvectors - compsystems - 12-27-2018, 04:50 PM
RE: Eigenvectors - parisse - 12-27-2018, 04:51 PM
RE: Eigenvectors - compsystems - 12-27-2018, 05:30 PM
RE: Eigenvectors - rawi - 08-21-2021, 07:48 AM
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