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Results tagged with na.numerical-analysis
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user 23900
Numerical algorithms for problems in analysis and algebra, scientific computation
4
votes
0
answers
424
views
Extreme eigenvalues of real symmetric matrix with main diagonal variance twice non-diagonal
Main question
Suppose there exists a random real symmetric $N \times N$ matrix $A$ with the main diagonal elements distributed according to $\mathcal N(\mu = 0, \sigma^2 = 4N)$, while all non-diagona …
- 385
9
votes
3
answers
6k
views
Eigenvalues of non-symmetric matrix and its transpose
What more can be said about the eigenvalues (especially the spectrum) of the $N \times N$ matrix ${\bf M} = {\bf A} + {\bf A}^T$ in terms of $\bf A$ if $\bf A$ is not symmetric and its eigenvalues are …
- 385
6
votes
1
answer
4k
views
Weyl inequalities for largest eigenvalue of matrix sum
The $k^{\rm th}$ largest eigenvalue (arranged in decreasing order) of the sum of two $N \times N$ Hermitian (real symmetric) matrices $\bf{A}$ and $\bf{B}$ can be stated using the Weyl inequalities as …
- 385
7
votes
2
answers
7k
views
Computational complexity of calculating the nth root of a real number
Several sources state that the computational or time complexity of square rooting is the same as that of multiplication (or division). See for example:
Jean-Michel Muller, "Elementary Functions: Alg …
- 385