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bio website uclue.com
location Knoxville, TN
age 61
visits member for 2 years, 6 months
seen Jul 25 at 2:18

Enjoys programming in Prolog.


Jun
24
comment Testing if a matrix is positive semi-definite
math.stackexchange.com/questions/753825/…
Jun
24
comment Testing if a matrix is positive semi-definite
The test you noticed in the library is likely based on the proposition that symmetric real matrix $A$ is positive definite if and only if each leading principle minor gives a positive determinant, something that could be checked by elimination without pivoting in exact arithmetic. The subtle difficulty of extending this to a semi-definite case has lured many authors into misstatement. I know the topic has been broached in a Math.SE Question, so I'll try to provide a link.
Apr
26
answered Optimization of prime factorization in C
Apr
24
reviewed Excellent Nodal DG method and limiters for hyperbolic conservation laws
Apr
24
reviewed Excellent Does the covariance matrix in Least Squares depend upon the input data?
Apr
24
reviewed Excellent Linear programming with matrix constraints
Apr
24
reviewed Excellent Crouzeix-Raviart Finite Element
Apr
24
reviewed Excellent Courant Friedrichs Lewy condition - how to get it?
Apr
24
reviewed Excellent last column of SPD matrix given it's spectral decomposition
Apr
24
reviewed Excellent Estimating hardware error probability
Apr
24
reviewed Excellent Convex objective function of matrix with prescribed determinant and trace
Apr
24
reviewed Excellent Least squares approximation question
Apr
23
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).
Apr
23
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.
Apr
23
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.