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Results tagged with na.numerical-analysis
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user 11142
Numerical algorithms for problems in analysis and algebra, scientific computation
1
vote
What software one needs to solve a big linear system on a small computer?
Mathematica will do this with no problems (actually, you can use your GPU to do it REALLY fast). Unlike Maple (apparently) there is no problem getting mathematica to use floating point computation, bu …
- 96.4k
2
votes
Simplex interval analysis
A typical operation is an affine transformation. The set of simplices is preserved by this, the set of balls is not.
- 96.4k
2
votes
Eigenvalues of monomial matrices
No. If $P$ is the matrix of a transposition (2 by 2) and $D$ is $diag(1, -1)$ the eigenvlues are imaginary.
- 96.4k
2
votes
Partitioned Runge-Kutta (Lobatto IIIAB)
Google says:
L. Abia and J. M. Sanz-Serna, Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems, Mathematics of Computation Vol. 60, No. 202 (Apr., 1993), pp. 617-634, doi:10.2307/21531 …
- 96.4k
6
votes
show that $ \frac{\Gamma(\frac{1}{24})\Gamma(\frac{11}{24})}{\Gamma(\frac{5}{24})\Gamma(\fra...
This follows from the discussion at and preceding page 31 in Campbell's book.
- 96.4k
4
votes
Accepted
Finding the smallest eigenvalues of a large, but structured, matrix
Well, if you add $c I$ to your matrix, for some reasonable value of $c,$ it will become nonsingular. As for the left inverse, since your matrix is sparse, to compute the backward iteration you can use …
- 96.4k
2
votes
Estimating the volume of a semialgebraic set from above
Here is an algorithm: partition $\mathbb{R}^n$ into cubes of side $1/k.$ For each cube $C_i$, use your favorite quantifier elimination algorithm to check whether the set $S$ intersects it. Then, your …
- 96.4k
1
vote
numerical methods for matrices (method of full reduction)
I have never heard of the "method of full reduction" (neither has Google), but a standard textbook on matrix computation is... "Matrix computation", by Golub and van Loan. For sparse matrix stuff (alm …
- 96.4k
1
vote
Numerical integration over 2D disk
An insufficiently well-known (so, perhaps slightly beyond the state of the art) integration algorithm can be found in the paper of O. Jenkinson and M. Pollicott entitled
"A dynamical approach to accel …
- 96.4k
3
votes
There must be a good introductory numerical analysis course out there!
Numerical analysis is a big subject... Stephen Boyd's Convex Optimization (available for download on his web page, or in two pound form from CUP) is a very lucid book, covering both applications and t …
1
vote
Computational complexity of integration in two dimensions
This paper seems to be a good reference:
Average Case Complexity of Weighted Integration and Approximation over $\mathbb{R}^d$ with isotropic weight, by Plaskota, Ritter, Wasilkowski.
Of course, the …
- 96.4k
1
vote
Error in Polynomial Root Finding Algorithm with Synthetic Division
Books have been written about this. The primitive implementation of this is going to be terrible, but some tweaks (see this wikipedea article, and references therein) work ok.
- 96.4k
6
votes
3
votes
Solving over-determined system of polynomials
I am not sure I understand what the ellipsis $\dots$ means in the last set of equations, since it seems that you only have pairs $l_i, u_i.$ If that is true, that means that there are $2^n$ possible v …
- 96.4k
14
votes
Accepted
How to compute $\sum_{x \in \mathbb{Z}^n} e^{-x^TMx}$ efficiently
You are trying to compute a multi-dimensional theta function, and this question is studied in depth in this 2003 Math. Comp. article by Deconinck, Heil, Bobenko, van Hoeij,and Schmies.
- 96.4k