(DM42) Matrix exponential
08-21-2023, 07:45 PM
Post: #21
 Albert Chan Senior Member Posts: 2,705 Joined: Jul 2018
RE: (DM42) Matrix exponential
(08-21-2023 07:03 PM)Gjermund Skailand Wrote:  A= [[ -49, 24][-64 ,31 ] ]
= [[1, 3] [2, 4]] × [[ -1, 0] [0, -17]] x INV[[ 1, 3][2, 4]]

exp(A)=[[1, 3] [2, 4]] × [[ exp(-1) , 0] [0, exp(-17)]] x INV[[ 1, 3][2, 4]]
= [[ -0.735759... , 0.551819... ] [-1.471518..., 1.103638...]]

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.
 « Next Oldest | Next Newest »

 Messages In This Thread (DM42) Matrix exponential - Gjermund Skailand - 08-11-2023, 09:56 PM RE: (DM42) Matrix exponential - Gil - 08-11-2023, 11:46 PM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-12-2023, 09:27 AM RE: (DM42) Matrix exponential - Albert Chan - 08-16-2023, 09:48 PM RE: (DM42) Matrix exponential - Albert Chan - 08-20-2023, 02:45 PM RE: (DM42) Matrix exponential - Albert Chan - 08-21-2023, 12:11 AM RE: (DM42) Matrix exponential - Gil - 08-12-2023, 10:01 AM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-12-2023, 11:38 AM RE: (DM42) Matrix exponential - Gil - 08-12-2023, 08:26 PM RE: (DM42) Matrix exponential - Gil - 08-12-2023, 08:55 PM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-13-2023, 10:23 AM RE: (DM42) Matrix exponential - Gil - 08-13-2023, 10:51 AM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-13-2023, 09:41 PM RE: (DM42) Matrix exponential - Gil - 08-13-2023, 09:46 PM RE: (DM42) Matrix exponential - Gil - 08-15-2023, 11:42 PM RE: (DM42) Matrix exponential - John Keith - 08-16-2023, 12:01 PM RE: (DM42) Matrix exponential - Gil - 08-16-2023, 12:45 PM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-16-2023, 04:38 PM RE: (DM42) Matrix exponential - Albert Chan - 08-21-2023, 11:49 AM RE: (DM42) Matrix exponential - Werner - 08-23-2023, 07:16 AM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-21-2023, 07:03 PM RE: (DM42) Matrix exponential - Albert Chan - 08-21-2023 07:45 PM RE: (DM42) Matrix exponential - Albert Chan - 08-23-2023, 07:55 PM RE: (DM42) Matrix exponential - Albert Chan - 08-23-2023, 09:39 PM RE: (DM42) Matrix exponential - Albert Chan - 08-26-2023, 10:20 PM RE: (DM42) Matrix exponential - John Keith - 08-27-2023, 04:46 PM RE: (DM42) Matrix exponential - Gil - 08-23-2023, 09:09 AM RE: (DM42) Matrix exponential - Albert Chan - 08-23-2023, 02:51 PM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-24-2023, 07:59 AM RE: (DM42) Matrix exponential - Werner - 08-24-2023, 01:14 PM RE: (DM42) Matrix exponential - Gjermund Skailand - 08-24-2023, 07:12 PM RE: (DM42) Matrix exponential - Gil - 08-28-2023, 08:57 AM RE: (DM42) Matrix exponential - Albert Chan - 08-28-2023, 01:10 PM

User(s) browsing this thread: 1 Guest(s)