Error correction in short packet.

On 20/05/2022 18:46, whit3rd wrote:
> On Thursday, May 19, 2022 at 3:31:23 PM UTC-7, John Larkin wrote:
> 
>> Yes, I work more by instinct and simulation. But my world is largely
>> nonlinear, where the math is basically impossible.
> 
> Identifying a problem as nonlinear IS math; it's obviously useful info,
> and the only deficiency is in the non-utility of common approximations.
> The math is not impossible, just... more difficult.

Quadratics are non-linear and taught as high school algebra. Cubics and 
their closed form solutions are seldom taught even at degree level.

A few other non-linear closed form solutions are known up to quartics. 
After that it is what Pade approximations are designed for.

They cause pure mathematicians to cross themselves and run out of the 
room. That aside on a good day you can get a workable and insightful 
approximations for real problems that are good enough for engineering.

Their first serious use was in taming highly divergent and hard won 
series expansions for high Mach number turbulent flow in aerospace.

The crucial point is that they are neither provably right nor exact but 
over some moderate range of your choosing can be made good enough for 
all practical purposes (or used as a guess for NR/Halley refinement).

-- 
Regards,
Martin Brown