Fazlollah Soleymani
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 Aug 2 comment How to use adaptive precision in matrix computations? Thanks for your comment. I do agree. However, I think some built-in functions of MMA already do such an action. An example is the function FindRoot[], which applies the precision of the input data (function and the initial guess) and then improve it per cycle. Also, applying the adaptive precision in matrix calculations (such as the above concrete question/idea) is very good in high precision computing environment. It should reduce the computational time dramatically for large scale problems. Aug 2 asked How to use adaptive precision in matrix computations? Jul 16 awarded Popular Question Apr 26 comment How to use Compile for accelerating matrix multiplications? Please write a code solution based on your tip. I am not familiar with your suggestion. Apr 26 comment How to use Compile for accelerating matrix multiplications? So, if you think there is any other way to speed up the process, I am happy to be informed. Furthermore, I cannot use CUDADot in my MMA. It fails to be fully downloaded and installed after 30 minutes. Any tips to accelerate the process is fully appreciated. Apr 25 comment How to find the index of a square matrix in Mathematica quickly? Dear J.M., I must compute the index for both types of matrices. Specially for inexact matrices. It would also be nice if an algorithm could produce $k$, $A^k$ and $A^{k+1}$ at the end of its run for all types of matrices. Apr 25 comment How to find the index of a square matrix in Mathematica quickly? Thanks. I meant if for example the rank is 2, then I need $A^2$ and $A^3$, i.e. the last two matrices in process of computations not the first two matrices. Apr 25 comment How to find the index of a square matrix in Mathematica quickly? Excellent idea. Can you check that why your technique cannot produce the result for a simple matrix in floating points arithmetic as follows: $n=100; a = RandomReal[{}, {n, n}]$. I faced with some errors such as "Transpose::nmtx: "The first two levels of the one-dimensional list {} cannot be transposed."". Apr 25 comment How to find the index of a square matrix in Mathematica quickly? Mr. Wizard, can you revise your code in order to give $A^k$ and $A^{k+1}$ as well. I mean I also need the last two matrices $A^{k+1}$ and $A^{k}$! Although $k$ is obvious but I do not want to compute them again because it might be time-consuming for large matrices! Can you give me a hand in this? Apr 25 comment How to find the index of a square matrix in Mathematica quickly? Thanks Mr. Wizard. It works good. Any improvement on the code will be appreciated. Apr 24 comment How to find the index of a square matrix in Mathematica quickly? I think the code is not working well, Mr. Wizard is right down here. For a random matrix, it sould give 0 while produces 5 as the $Ind(A)$. Apr 24 comment How to find the index of a square matrix in Mathematica quickly? You are totally right Mr. Wizard, the codes sounds to be incorrect. For the 500*500 example of you, the answer must be $Ind(A)=0$. Because $A^0$ and $A^1$ agrees in terms of rank. So is there any bug here? Apr 24 comment How to find the index of a square matrix in Mathematica quickly? Yes, your answer always gives 2 as the output by varying $n$, while the output of Szabolcs's code is correct and is what I want. Your technique to accelerate the process is nice, but currently not working. Apr 24 comment How to find the index of a square matrix in Mathematica quickly? I think Mr. Wizard answer needs some revision. I mean the answers are not the same. For instance, check the following sample examples: Clear["Global`*"] SeedRandom[1234]; n = 500; A = RandomReal[{}, {n, n}]; Length@NestWhileList[A.# &, A, MatrixRank[#] == MatrixRank[#2] &, 2] // AbsoluteTiming Length@NestWhileList[{A.#[[1]], MatrixRank@#[[1]]} &, {A, -1}, #[[2]] == #2[[2]] &, 2] // AbsoluteTiming Apr 24 asked How to find the index of a square matrix in Mathematica quickly? Apr 6 comment How to draw Fractal images of iteration functions on the Riemann sphere? Thanks. An excellent answer. Just one note. There might be some diverging points (black areas) in the fractal picture for some test problems. On the other hand, we used a color correspond to a point in a sphere or a rectangular domain. So, the domain of working (I mean the mesh of points) are finite. So is it possible to count the number of diverging points? I mean it would be nice to have the percentage of diverging points for each fractal picture. Is it possible to count the number of diverging points in your implementation? Apr 5 awarded Nice Question Mar 11 comment How to use Compile for accelerating matrix multiplications? So, is there any other way such as parallelization? Mar 11 comment How to use Compile for accelerating matrix multiplications? As far as I know, for smin and smax, Mathematica 8 uses the Arnoldi algorithm with at most 1000 MaxIterations. However, this part is quite fast. Do you think, is there any way to use Compile for speeding this code up? Mar 11 asked How to use Compile for accelerating matrix multiplications?