Is the only reason a really small h is worse because of floating point rounding?
asheng2
When referring to relative error in the graph, what is the error "relative" to? If we were to plot the absolute error, instead of seeing the error shoot back up, would we instead get a plateau?
Midoriya
So how do we pick h? Do we just try many different values and see where the difference converges?
frogger
Why does the error function seen in the graph change so quickly? I would think that for "reasonable" functions, the impact of changing h slightly would be relatively small.
dl123
Do we just test bunch of h and pick the one with smallest error?
Coyote
Is it possible to optimally pick h based on our function or do we have to sort of "spray and pray" with several different h values?
ant123
How would we determine if h is "too small?" And regarding relative error, what are we saying the error is relative to?
Oh_skr
If we don't know the correct/true derivative of a function, how would we know the relative error?
anon
Does h change very drastically from function to function or is there a default value that could work decently for a majority (or a certain subset)?
corgo
How can we know when we have a relative error if we have no idea what the actual function looks like?
Murrowow
Is this similar to aliasing where if the value you choose is too small/different, it would cause the values to be incorrect.
Is the only reason a really small h is worse because of floating point rounding?
When referring to relative error in the graph, what is the error "relative" to? If we were to plot the absolute error, instead of seeing the error shoot back up, would we instead get a plateau?
So how do we pick h? Do we just try many different values and see where the difference converges?
Why does the error function seen in the graph change so quickly? I would think that for "reasonable" functions, the impact of changing h slightly would be relatively small.
Do we just test bunch of h and pick the one with smallest error?
Is it possible to optimally pick h based on our function or do we have to sort of "spray and pray" with several different h values?
How would we determine if h is "too small?" And regarding relative error, what are we saying the error is relative to?
If we don't know the correct/true derivative of a function, how would we know the relative error?
Does h change very drastically from function to function or is there a default value that could work decently for a majority (or a certain subset)?
How can we know when we have a relative error if we have no idea what the actual function looks like?
Is this similar to aliasing where if the value you choose is too small/different, it would cause the values to be incorrect.