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Mar
11
asked How to use Compile for accelerating matrix multiplications?
Feb
26
comment How could we define a function recursively?
Thank you ssch. The second way that you describe is my question. That is, the old beta is in the right side and the new beta must be obtained as the left beta. Therefore, in your second part of the answer, there are still some drawbacks in my idea. Since, I need the final formula as an iteration function (similar to the case of Sign[z]), not to be defined numerically as you have done for four nested values. Is there any way to define this recursive function by two parts I mean the first part calculate a new value (a new value) and the second part update beta?
Feb
26
asked How could we define a function recursively?
Feb
24
awarded  Commentator
Feb
24
comment How to accelerate updating some parts of sparse matrices?
In my idea, the best way is to extract the diagonal elements of the matrix inverse, and then update your matrix $mat$. In such a way, the norm of the matrix $Id-A.mat$ will decrease much more and with one replacement you might obtain the best possible approximate inverse. The only problem is that how to extract or find the diagonal entries of the matrix inverse very fast for a very large sparse matrix!
Feb
24
comment How to accelerate updating some parts of sparse matrices?
I think the above piece of codes fail even when we test a 300*300 sparse matrix. I mean sometimes in my MMA 8, it gives the results and sometimes when I increase $num$ to 3 (for instance), it fails and the MMA generates a beep!
Feb
21
revised How Simplify and Assume can be combined on matrix products?
added 3 characters in body
Feb
21
asked How Simplify and Assume can be combined on matrix products?
Jan
3
awarded  Supporter
Nov
23
comment How to draw Fractal images of iteration functions on the Riemann sphere?
Thanks, the problem is that when we reduce PlotPoints or ImageResolution, the quality gets down dramatically. I am looking for a fast way to obtain high quality pics, with small space size, just like the one given in the question. Rasterize@... is a good choice, but it disables the feature of rotating the 3D pic, and also gets the quality lower.
Nov
22
comment How to draw Fractal images of iteration functions on the Riemann sphere?
Thanks for your response. There are two problems. 1. How can one zoom in on a particluar place on this sphere without lowering the quality to observe the fractal behaviour of the method? 2. The "spcae size" of the output image? In fact, how one can save as the output fractal image with low "disk size" without lowering the quality in EPS format? For example, for $n=8$, its size is more than 2MB!
Nov
22
comment How to draw Fractal images of iteration functions on the Riemann sphere?
Thanks for your reply, but there are big white circles at the middle of each basin. They should not be here. Please rotate your image, and then you will see the incomplete fractal image. Can you solve this drawback?
Nov
22
awarded  Teacher
Nov
22
asked How to draw Fractal images of iteration functions on the Riemann sphere?
Nov
22
answered Is there any way to obtain an approximate inverse for very large sparse matrices?
Sep
12
revised How to discretize a nonlinear PDE fast?
deleted 1 characters in body
Sep
12
comment How to discretize a nonlinear PDE fast?
You solved Subscript[u, t] + u Subscript[u, xx] = c Subscript[u, xx]. Please consider solving the following NPDE instead: Subscript[u, t] + u Subscript[u, x] = c Subscript[u, xx].
Sep
11
comment How to discretize a nonlinear PDE fast?
In fact, it should be the nonlinear burgers equations.
Sep
11
comment How to discretize a nonlinear PDE fast?
I revised the question, now please give some comments.
Sep
11
revised How to discretize a nonlinear PDE fast?
added 24 characters in body