# Tag Info

### 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 ...
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### 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. ...
Accepted

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)))  ...
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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 ...