(DM42) Matrix exponential

[Albert Chan]

(08-23-2023 09:09 AM)Gil Wrote:  What is the meaning (perhaps with an example) of the function/command MAXAB(X)?

MAXAB(X) is from JFG "Math Pac 2" - Version 2B Feb. 2021
MAXAB = Array Element Maximum Absolute Value. (Perhaps it should be named MAXABS)
It has a side effect of saving where element is located.

>mat disp x
-5.46969688594
22010.2875425
-22141314.9958

>maxab(x), arow, acol
22141314.9958            3      1
>minab(x), arow, acol
5.46969688594            1      1

Quote:P=MAX(0,IROUND(LOG2(MAXAB(X)))+10)

This is to make sure X/2^P elements size at most ε = 2^(-9.5) ≈ 0.00138

expm1(ε) = ε + ε^2/2! + ε^3/3! + ε^4/4! + ...

If I drop..., expm1 relative error ≈ (ε^5/5!)/ε = ε^4/120 ≤ 3.0E-14, less than machine epsilon.

Note: matrix multiply is a dot product of row and col, it really depends on cell values.
Above is *very* rough estimate of relative errors. (and, only if ε is truly small)