ebrahimina

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These are questions asked by ebrahimina

why do solve and fsolve have different results?

solve-fsolve.mw

If A is an m × n matrix and B is a p × q matrix, then the Kronecker product C = A ⊗ B is the mp × nq block matrix. Assume I have matrix C and want to find matrix A and B. This problem has known solution called "Nearest Kronecker Product". So I just need a function like this: A,B:=NearestKroneckerProduct(C)  which minimizes ||C - A ⊗ B||F  where denotes frobenius norm. 

Here is an Image that shows a mathematica code:

I took it from the link below:

https://mathematica.stackexchange.com/questions/91651/nearest-kronecker-product

Also there is a matlab code:

https://gist.github.com/tholden/58dd9a8991daa750ae36a633fe7060a4/revisions

can you convert mathematica code to maple?

I want to divide each row of Marix A by diagonal element. In for loop, when I assign dividing results to the letter , the type of A still remains matrix, but if I choose another letter (like B) results are stored in Table. Why? How can I assign to a matrix?

Also I can't figure out why maple doesn't show elements of table(see worksheet file).

I should notice that my main problem is assigning not dividing.

worksheet.mw

 

How can I compute MatrixInverse, MatrixMultiply and eigenvalues(eigenvectors) faster? are there any procedures or commands that can be used instead of those three command mentioned before to speed up calculations?

1.mw

In the above document, digits must be 30.

I have a eigenvalue problem like:

[FF1]* {w}=N^2 *[FF2] *{w}

[FF1] and [FF2] are a*b matrices (non square matrix) , {w} are vectors(eigenvectors) and the values of N are eigenvalues.

I want to obtain eigenvalues and eigenvectors by computing Moore-Penrose pseudo-inverse of [FF2] and do the procedures below :

[FF2]^-1 * [FF1] *{w} =N^2 *{w}            ,        (assume  [FF2]^-1   is Moore-Penrose pseudo-inverse of [FF2]   )

[FF2]^-1 * [FF1] = [FF3]  ,  ( [FF3] is a b*b matrix- squre matrix) 

so  [FF3] *{w}=N^2 *{w}

then I can use LinearAlgebra[Eigenvectors](FF3) to get eigenvalues and eigenvectors. 

I know that Moore-Penrose pseudo-inverse of [FF2] * [FF1] isn't equal to Identity matrix. [FF2]^-1 * [FF1] <> [ I ] . But assume it can be. ( I have a solution for this problem) . 

My biggest problem is [FF2] and [FF1] are large-scale sparse matrix and it takes hours or several days that maple can compute Moore-Penrose pseudo-inverse of [FF2]  and also LinearAlgebra[Eigenvectors](FF3). 

Main question : can I compute Moore-Penrose pseudo-inverse and LinearAlgebra[Eigenvectors]  by using Parallel Programming?  if the answer is yes , how? give me an example please.

if the answer is No , is there any way (any algorithm) to find the inverse of a large non-sqaure matrix or eigenvalues of a large matrix faster?

please introduce some books for parallel programming in maple or general.

Thanks.

1.mw

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