1,637 reputation
1321
bio website uclue.com
location Knoxville, TN
age 61
visits member for 2 years, 3 months
seen 6 hours ago

Enjoys programming in Prolog.


6h
reviewed Excellent Nodal DG method and limiters for hyperbolic conservation laws
6h
reviewed Excellent Does the covariance matrix in Least Squares depend upon the input data?
6h
reviewed Excellent Linear programming with matrix constraints
6h
reviewed Excellent Crouzeix-Raviart Finite Element
6h
reviewed Excellent Courant Friedrichs Lewy condition - how to get it?
6h
reviewed Excellent last column of SPD matrix given it's spectral decomposition
6h
reviewed Excellent Estimating hardware error probability
6h
reviewed Excellent Convex objective function of matrix with prescribed determinant and trace
7h
reviewed Excellent Least squares approximation question
14h
comment Large binary programming problem
Look for papers by Patrick Ostergard, from 2000-2002. He considers problems with positive integer weights on the vertices (nodes).
15h
comment Large binary programming problem
Known in the literature as maximum weight clique problems, these are NP-hard as a general class. Your problem size seems daunting if an exact solution is needed, but studies have proceeded along lines of faster exact solutions of smaller problems and better approximate solutions with larger problems.
19h
comment Large binary programming problem
Do we know $A$ is symmetric? Are its diagonal entries all 1's?
Mar
25
comment Fibonacci, variation on the theme
I suspect we don't need to store a lot of $a(p)$ values to get a benefit in sieving, but you've done more computations than I have. How does the number of solutions between $10^N$ and $10^{N+1}$ seem to behave as $N$ grows?
Mar
22
revised Fibonacci, variation on the theme
Added links, some details of sieving procedure, notion of "primitive" solutions
Mar
22
answered Fibonacci, variation on the theme
Mar
20
comment Fibonacci, variation on the theme
That's a valid doubt. It suggests one might benefit by doing some Fibonacci steps of modest prime lengths to sieve out the bulk of numbers to be tested.
Mar
13
comment Fibonacci, variation on the theme
It looks like the computation of Fibonacci number $F_n$ is done from scratch with each call to fibmod. So if instead you kept two variables holding $F_{n-1}$ and $F_n$, then each iteration would only require an addition and a reduction mod $n$, with a bit of shuffling of values to keep the last two Fibonacci numbers for the next iteration.
Mar
9
reviewed Reviewed Solving a non linear equation and iterating for various values in python
Mar
9
comment Solving a non linear equation and iterating for various values in python
As a practical matter, how would one know how many solutions to expect? Some thoughtful analysis is usually required even for the case of a real polynomial, in that the number of real solutions may be less than the degree (even setting aside issues of multiplicity of roots). In a wider setting there could be infinitely many solutions for one unknown in one equation.
Feb
10
reviewed Reject suggested edit on Integration of an indefinite integral: matlab precision problem