1
vote
0answers
14 views

Why more smooth the function the more precise finite difference method?

As the title, Why more smooth the function the better finite difference method? I guess that if the function is smooth we can better approximate with Taylor series, but formally how this helps? ...
1
vote
1answer
36 views

Finite differences coefficients

I'm interested in deriving a forward finite difference approximation for the gradient of a function, $f(x)$, at the point $x = x_i$ using $k+1$ points. If the spatial domain is uniformly discretized, ...
0
votes
1answer
66 views

Analytical way of describing centred difference coefficients

I am trying to find an analytical way to describe the finite difference coefficients of various degrees of accuracy of centred difference schemes that approximate the second derivative. For example, a ...
66
votes
3answers
2k views

Is the derivative the natural logarithm of the left-shift?

(Disclaimer: I'm a high school student, and my knowledge of mathematics extends only to some elementary high school calculus. I don't know if what I'm about to do is valid mathematics.) I noticed ...
3
votes
1answer
870 views

Computing the elements of a Hessian matrix with finite difference

I have a generic function $g(x)$ where $x$ is an 6-dimensional vector. Now I want to compute the Hessian of this function for a point $x_0$. What is the most efficient way to do this? Can I do this ...