a****o
发帖数: 42 | 1 CG is for conjugrate gradient method, once CMU has a very complete report o
on this, preconditioner has many method, but frankly a care-free conditioner
has never been verified in my experience. You should be able to get
the related information from most advanced text book on CFD. One of
such book is by a stanford prof in 1995 (?), published by Springer,
with name of computational fluid dyanmics ...
I have no experience with FFT or things related, but I do suspect that solving
matrix problem can | r****y
发帖数: 1437 | 2
我上文说到的那个迭代次数几乎独立于矩阵大小的是专指对Toeplitz矩阵,
加上circulant矩阵的preconditioner. Toeplitz矩阵指任何一个对角线上的所有元素
都相等的对称矩阵, circulant矩阵的就是轮换矩阵. 对于一个Toeplitz矩阵,
构造相应的circulant矩阵(比较流行的有两种方法), 然后进行迭代, 试验不同大小
的矩阵, 就可以看到上面的结果. 我对这个的了解来自上个学期做的term project,
觉得这个preconditioner很有意思. 你可以自己试一下, 找任意circulant矩阵C,
任意相应大小的矢量v, 假设C的第一列是c1, 那么
fc1 = fft(c1)
temp = fc1*v*fc1'
vc = ifft(temp)
可以证明 vc = Cv, 这里fft, ifft 对应快速Fourier和反Fourier变换.
至于CG和preconditioner的书, 我想CFD的并不是最好的, 还是看那些专门
【在 a****o 的大作中提到】
: CG is for conjugrate gradient method, once CMU has a very complete report o
: on this, preconditioner has many method, but frankly a care-free conditioner
: has never been verified in my experience. You should be able to get
: the related information from most advanced text book on CFD. One of
: such book is by a stanford prof in 1995 (?), published by Springer,
: with name of computational fluid dyanmics ...
: I have no experience with FFT or things related, but I do suspect that solving
: matrix problem can
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