(DM42) Matrix exponential

[Albert Chan]

(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.