(DM42) Matrix exponential
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08-21-2023, 07:45 PM
Post: #21
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RE: (DM42) Matrix exponential
(08-21-2023 07:03 PM)Gjermund Skailand Wrote: A= [[ -49, 24][-64 ,31 ] ] I was doing expm1(A) = exp(A) - 1 (= identity matrix). Adjusted, both agreed. Quote:But my implementation on HP50g using double binary floating point fails. This is why example is nasty, if we just simply do e^A = 1 + A + A^2/2! + A^3/3! + ... The terms blows-up passes true answer. (Matrix A already bigger than final sum!) A^16/16! ≈ [[6977251.9061, -3488625.95305], [9303002.54147, -4651501.27073]] A^17/17! ≈ [[-6977251.9061, 3488625.95305], [-9303002.54147, 4651501.27073]] No. the 2 terms are not exactly negate of the others. But, catastrophic cancellation made the sum meaningless. |
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