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I want to compute the action of matrix exponential on a vector. My matrix $ B$ is of a very large size and it is sparse, e.g., it is written as follows: size = 350; vector0 = Range[0., 300., 300./(size – 1)]; B0 = NDSolve`FiniteDifferenceDerivative[2, vector0, “DifferenceOrder” -> 20][“DifferentiationMatrix”]; B = SparseArray@KroneckerProduct[B0, B0]; vector =Read more

Given a normal matrix, for example m = Array[a,{4,4}] which has dimensions {4,4}, I can partition it by using: m2 = Partition[m,{2,2}], which has dimensions {2,2,2,2}. Now, if m is a sparse array, for example: m = SparseArray[Table[{i,i}->i,{i,1,4}],{4,4}] I would like to be able to partition it in a similar manner but with the resultRead more

I would like to construct a rectangular matrix which doesn’t have a decomposition into a product of a sparse and a small matrices. It is easy to see that a random matrix doesn’t have such a representation, but I’d like to find an explicit example. More precisely, I want to find an explicit matrix $Read more