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Jul
25
reviewed Reviewed SVD of large block-hankel matrix
Jul
25
comment SVD of large block-hankel matrix
I suspect you are suggesting that for low-rank approximation, only the largest singular values are needed and can be found less expensively than the full decomposition. However your brief post leaves much to the Readers imagination.
Jul
25
reviewed Reviewed Modern C++ in scientific computing?
Jul
25
comment Modern C++ in scientific computing?
Welcome to scicomp.se! If you add links or cite some articles/books/blog-posts that discuss this library for scientific computation, I'll happily upvote your Answer!
Jul
14
reviewed No Action Needed Why are Runge Kutta and Euler's method are so different?
Jul
9
comment How to avoid overflow error in program that computes product of two numbers, such that when one is big enough to cause overflow, other is $0$?
Sure, if $h(x)$ is precisely zero (or if $g(x)$ is), then their product is precisely zero. Otherwise the relative accuracy of $g(x)\cdot h(x)$ depends on getting relative accuracy in both factors. Aiming at the computation of the logarithms, rather than $g(x),h(x)$ themselves, is a fairly common way of managing the extremes of magnitudes. I would adopt just such a strategy if $h(x) = \operatorname{erf}(a) - \operatorname{erf}(x)$ for large $x \gt a$.
Jul
8
comment How to avoid overflow error in program that computes product of two numbers, such that when one is big enough to cause overflow, other is $0$?
It's unclear why you think the product $g(x)*h(x)$ should be approximately zero, just because $h(x)$ is close to zero. After all you open by saying that in these cases $g(x)$ is very large (causing overflow). Perhaps the crux of the matter is how to compute $g(x)$ to avoid overflow. Can we instead compute $\ln g(x)$? Then the rest of the computation could be $f(x) = exp(\ln g(x) + \ln h(x))$, and this would likely be more numerically stable.
Jul
8
reviewed Reviewed Relaxation - spreadsheet solution to recursive algorithm
Jul
8
comment Relaxation - spreadsheet solution to recursive algorithm
You only need to break the "circular reference" in one place. A0 and A4 are given (constants), so we can omit them from the circle (i.e. just put their fixed values into the computation; they don't depend on A1,A2,A3 whatsoever. So (for example) put a starting value in for A1 in (for the sake of irony) cell A1, the formula for A2 in A2, and the formula for A3 in A3. Then in cell B1 (next to cell A1), put the formula for A1. By updating the value in cell A1 for A1 with the computed value in cell B1, you can observe the successive convergence of entries.
Jun
30
comment Selecting most scattered points from a set of points
Would you like to post the coordinates for the 19 points in your example? I could then show you the difference between the maximum sum of distances and maximum minimum distance objectives.
Jun
30
answered Selecting most scattered points from a set of points
Jun
29
comment Selecting most scattered points from a set of points
A similar problem for a continuous region was posed, but not answered, at MathOverflow: n-Cats-in-a-Bed Problem: Picking n points in a given planar domain to maximize the sum of their pairwise distances.
Jun
29
comment Selecting most scattered points from a set of points
For the case $M=2$ see this from StackOverflow: Algorithm to find points that are furthest apart — better than O(n^2)?.
Jun
28
comment Optimization with matrix determinant as constraint
How many $\mathbf{E_i}$ vectors are involved?
Jun
28
reviewed Reviewed BLAS, LAPACK or ATLAS for Matrix Multiplication in C
Jun
28
comment BLAS, LAPACK or ATLAS for Matrix Multiplication in C
If matrix multiplication is all that is desired, yes, BLAS Level 3 seems a good place to start. StackOverflow has this now closed Question from 2010 on requesting documentation/getting started info. You may find the interface appears more complicated than necessary, which is partly a result of historical compatibility with Fortran callers.
Jun
28
answered Simple Path to Route Algorithm
Jun
26
reviewed Reviewed Solve $AX = B$ where $X^T X = C$
Jun
26
comment Solve $AX = B$ where $X^T X = C$
Are you suggesting that $X$ is a matrix but not necessarily a square matrix?
Jun
26
reviewed Reviewed Ideas on how to search nearby geospatial data fast