[Unsolved] Gateaux and Frechet differentiation

[warped vortex]

Derivation?

Do u mean differentiation

[tardy scaffold]

Yes 😁 got lost in translation. Will edit

Gateaux and Frechet differentiation

[warped vortex]

what course are you doing this for

So I can know what to use

[tardy scaffold]

It is called simply Calculus 2. We did Integration and metric spaces, Banach, L2 spaces and the last chapter, "Differentiation in banach spaces" (very brief) contained these two definitions, gradients and few multilinear examples.

Thank you for the good will

[warped vortex]

Ok alright so I can apply some basic funct anal

[tardy scaffold]

That would be amazing

[warped vortex]

K I had to do smth

But im back

Could you give me the definitions ur book gave?

Anyways

For the norm

[tardy scaffold]

yes I can, give me a second

[warped vortex]

so since I’m gonna assume ur working with in over the reals

then norm here is gonna be

The norm of real number space

Which is just the magnitude of the vector

Or length

[tardy scaffold]

Here's the operator norm, mentioned before the definition

This is the definition for the Gateaux

And here for Frechet

Sorry, I didn't have an option to crop the images, but I assume, you'll know which part of the txt is the definition

[warped vortex]

Ah k

So it’s just the standard definition

Of each

[tardy scaffold]

😁 hope that makes it easier

[warped vortex]

Ok well now lemme just

Do the actual calculations

[tardy scaffold]

take your time

[warped vortex]

ok frankly for the frechet derivative I got D(f(x,y) )= infinity when y = x^2 and 0 otherwise

But I’m not sure

At all

[tardy scaffold]

hmmm, they tend to give challenging exercises. would you mind sharing nevertheless? I believe it would still help me to get throught some (for me) critical points

I appreciate in any case that you tried!

[tardy scaffold]

[Unsolved] Gateaux and Frechet differentiation