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bio website alexflint.weebly.com
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visits member for 1 year, 10 months
seen Oct 5 at 13:30

I work on the computer vision behind augmented reality applications for mobile phones at a startup called Ogmento in New York City.


Sep
24
awarded  Autobiographer
Jul
23
awarded  Commentator
Jul
23
comment Software tools for medium-scale systems of polynomial equations
@wonko Each $f(x)$ is a polynomial so yes twice differentiable but not convex. Each $f(x)$ has total degree 7 or lower. The code to generate the problem is here: bit.ly/WCYM0H. A numerical dump of the cost function is here: bit.ly/1qA2kOp.
Jul
23
comment Software tools for medium-scale systems of polynomial equations
@wonko Thanks for the NEOS link - I was not aware of that service before. I would certainly value your help with this optimization problem (thanks!), and I'm happy to provide more details. I'm attempting to solve a problem in visual inertial navigation where the variables represent the trajectory of a device and the cost terms are related to sensor measurements captured over time by that device. Each term of the cost function looks like $(f(x)-y)^2$ where $y$ is a sensor measurement. There are no constraints on the variables except that they must be real numbers.
Jul
22
comment Software tools for medium-scale systems of polynomial equations
@wonko I am very much interested in global optimization rather than gradient-based iterative optimization in this problem. Methods like Gauss-Newton / Levenberg-Marquardt will not work. Having said that, are there any general purpose global optimization tools you would recommend?
Jul
22
comment Solve Multivariate Polynomial
How about action matrix methods where you compute a multiplication matrix and find its eigenvalues? Do you consider these as part of Grobner basis methods?
Jul
22
revised Software tools for medium-scale systems of polynomial equations
minor typo
Jul
22
asked Software tools for medium-scale systems of polynomial equations
Apr
7
awarded  Scholar
Apr
7
accepted Distance between two points in UTM coordinates.
Apr
3
asked Distance between two points in UTM coordinates.
Oct
18
asked is there a polynomial-form minimal representation for SO(3)?
Jul
16
comment Cholesky decomposition of $A+kI$ given Cholesky decomposition of A
Have updated the question. If $k$ is negative then $A+kI$ may or may not be positive definite. For an example that is positive definite, take $A=2I$ and $k=-1$.
Jul
16
revised Cholesky decomposition of $A+kI$ given Cholesky decomposition of A
deleted 2 characters in body
Jul
16
asked Cholesky decomposition of $A+kI$ given Cholesky decomposition of A
Feb
13
comment Compute the covariance of $R_2 R_1^T$ where $R_2$ and $R_1$ are rotation matrices with Gaussian uncertainty
@Sasha: Apologies again! I believe the question is now clear.
Feb
13
revised Compute the covariance of $R_2 R_1^T$ where $R_2$ and $R_1$ are rotation matrices with Gaussian uncertainty
edited body
Feb
13
comment jacobian involving SO(3) exponential map: $\log(R \exp(m))$
Thanks @AviSteiner. BTW I have found in numerical experiments that the relationship (for SO(3)) between $m$ and $y=log(R*exp(m))$ is either affine $y=Am+b$ or extremely close to affine for all the cases that I've tried. It could be that some of the terms in the expansion you point to disappear for the special case of SO(3).
Feb
12
asked jacobian involving SO(3) exponential map: $\log(R \exp(m))$
Feb
12
awarded  Editor