Recent content by Teg Veece

Thanks for the quick reply. Wouldn't adding a constant to the denominator not have a significant effect on the final result depending on what I set c to be? Like c = 0.01 would be a very different solution from c=10. I know that they have a similar problem with singularities when...

I have an equation that relates two variables: k(\mathbf{x},\mathbf{x}') =exp(-(\mathbf{x}-\mathbf{x}')^2) If I want to determine the value of this equation where x' is kept constant and x is actually the set of every real number then I can express the function as the integral where the...

I have a velocity field that is static in time. At every location, x, there is a corresponding velocity vector. I'm trying to work out the displacement of a particle after T seconds if I drop it into the velocity field at time t=0 and at location x_0. I was thinking something along the lines...

I found something on the wikipedia page saying it's error is bounded by O([2N]^{-k}/k) for a k-times differentiable integrand. I'm not sure what a k-times differentiable integrand is exactly but, at a guess, is a function like x^2+2x+5 differentiable 3 times and x^9+2 differentiable 10 times...

It does actually. Thanks for that. Do you know what the error is for a Clenshaw-Curtis quadrature?

Hey, I'm using a quadrature to estimate the integral of a function. Intuitively, I know that if the function is a very smooth function, the quadrature will perform well at a low order (few samples). If however, the function in more complex, I'll need to sample it more frequently for the...

Or I guess in other words, what I'm asking is it is possible to determine the mean value of the Gaussian distribution along a line segment like in the diagram below?

I've been trying to evaluate an integral for the last few days now and it really has me stumped. I was hoping that maybe someone here would be able to help me out. So the function, cov(x,x'), is fairly basic. It's called a squared exponential covariance function and it evaluates the covariance...