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Feb
3
comment How can we draw a stencil for discretization of PDEs?
Wow. Thanks. The 3D plot is totally useful for showing the discretizations. Just one quick note. Usually, for the 2D case, the node left to (i,j) is (i-1,j) and the right one is (i+1,j). But here, it is vice versa. Although the plot is correct, I wished to know that how we can reverse this sorting of indices in the code.
Feb
3
accepted How can we draw a stencil for discretization of PDEs?
Feb
3
accepted How to find the index of a square matrix in Mathematica quickly?
Feb
3
comment How can we draw a stencil for discretization of PDEs?
I tried but I failed to build such a piece of code.
Feb
2
comment How can we draw a stencil for discretization of PDEs?
Thanks. I did as you suggested.
Feb
2
comment How Simplify and Assume can be combined on matrix products?
So, how this works in practice. I mean can you revise my above code so as to keep the commutativity while simplifying the Taylor expansion?
Feb
2
accepted How to use Compile for accelerating matrix multiplications?
Feb
2
accepted How to use adaptive precision in matrix computations?
Feb
2
accepted How to speed up filling a matrix as much as possible in a loop?
Feb
2
accepted How to extract and compute on the diagonal entities of a sparse matrix very fast?
Feb
2
comment How can we draw a stencil for discretization of PDEs?
I would like to show the indices, i, j, k and the step-sizes along the three dimensions x,y,z. Furthermore, it would be of interest if e.g. the nine central nodes are colorized with black color and the other nodes are empty.
Feb
2
asked How can we draw a stencil for discretization of PDEs?
Jan
26
awarded  Scholar
Jan
26
accepted How to draw Fractal images of iteration functions on the Riemann sphere?
Jan
26
accepted Computing the logarithmic spectral norm rapidly
Jan
26
comment Computing the logarithmic spectral norm rapidly
Great. Thank you so much.
Jan
25
comment Computing the logarithmic spectral norm rapidly
Wow. It gives correct results, but may you please let us know where are "the limit" or "the identity matrix" (which are in the mathematical definition) are?
Jan
25
asked Computing the logarithmic spectral norm rapidly
Jan
20
comment How to speed up filling a matrix as much as possible in a loop?
Yes, the cost of calculating the function is the dominant one. But, when the size of the system becomes large, computing the function evaluations and then filling the matrix becomes slow again. I am trying to solve a discretization nonlinear system resulting from a PDE with the above approach. But for large sizes, it is slow. Maybe, it would be better to incorporate the notion of sparsity in your nice answer.
Jan
19
comment How to speed up filling a matrix as much as possible in a loop?
I have a related observation. For large systems ($n>200$), once again filling the matrix is slow. Do you have any ideas to fill the matrix for sparse cases also too fast?