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Results tagged with na.numerical-analysis
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user 119995
Numerical algorithms for problems in analysis and algebra, scientific computation
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Complexity of singular value decomposition using matrix multiplication oracles
Suppose I have an $n\times m$ real matrix $A$, $n\ll m$ with full row rank $(\mathrm{rank}(A) = n)$. I have an oracle that can compute $Ax$ or $A^T y$ for any $x\in \mathbb{R}^m, y\in \mathbb{R}^n$. H …
- 662
1
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0
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Upper bound $\sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j})$
Let
$$p_{i,j} = \frac{\sum_{l=i}^{i+j-1} {l-1 \choose i-1} {m+n-l \choose m-i}}{{m+n \choose n}}$$
I am interested in approximating/upper bounding the sum
$$ \sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j …
- 662