New answers tagged linear-algebra
12
votes
Time and memory required to diagonalize a 18000 by 18000 matrix using numpy in python
A 20000 by 20000 double-precision complex matrix requires
$20000 \times 20000 \times 8 \times 2=6.4 \mbox{gigabytes}$
of RAM. The LAPACK routines ZHEEV that will do the work for you will store the ...
- 18.2k
4
votes
Rank-1 correction of matrix exponential
There is work on low-rank updates of matrix functions, for instance this one:
Beckermann, Bernhard; Kressner, Daniel; Schweitzer, Marcel, Low-rank updates of matrix functions, SIAM J. Matrix Anal. ...
- 10k
4
votes
Accepted
How to optimize an approximated matrix multiplication?
This is a linear least squares problem if you just look at it the right way. Write
$$
B = (I-aX)^{-1},
$$
then $X = \frac{1}{a}(I-B^{-1})$ and
$$
(I-aX)^{-1}XA = B\frac{1}{a}(I-B^{-1})A = \frac{1}{...
- 52.4k
3
votes
Powers of convergent DPR1 matrices in $O(d)$ time?
It is not necessary to compute $A^k$ in your case. You can do a matrix-vector product with $A=D+pq^T$ in about $5d$ operations, and so multiplying with $A^k$ via
$$
A^k v = A (A (A \cdots (Av)))
$$
...
- 52.4k
3
votes
Accepted
Faster than forward substitution?
Let's assume that the size $m$ of the individual blocks is fixed, but that the number of blocks $n$ grows. Then the one-step-at-a-time algorithm takes $O(m^3n)$ operations if you chose to invert the ...
- 52.4k
3
votes
Faster than forward substitution?
I am not an expert in the field, but since there are no other answers at least I can suggest you a keyword to start a literature search: "parallel-in-time integration methods". This is a ...
- 10k
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