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comment Determine Toeplitz matrix
One way is to solve $\min \|A-X\|$ such that $X \in \mathcal{T}$, where $\mathcal{T}$ is the set of Toeplitz matrices (this is a linear structure, so this particular problem can be solved using an SDP solver).
1d
comment I have a very large sparse matrix, 'A', in Ax = b. What work in advance of getting 'b' can be done to reduce solving time?
What do you mean by "missing constant values"? Are you saying that you have a large sparse matrix say $A$ and you wish to linear systems of the form $Ax=c$, where $c$ is some integer (a "constant" as you call it)? Please rewrite the question to make it more precise.
May
2
comment Not especially famous, long-open problems which anyone can understand
This recent preprint arxiv.org/abs/1604.08657 claims to "nearly settle" this conjecture....
May
2
comment Open problems in Euclidean geometry?
I just saw this: arxiv.org/abs/1604.08657 which claims to "nearly settle" the cited open question...
Apr
30
comment $k$-th diagonal element of an inverse matrix $(\textbf{H}^{\dagger}\textbf{H})^{-1}$
math.stackexchange.com may be a better place for this question.
Apr
28
comment Does it make sense to compare sets (polytopes) with different dimensions?
Clearly, by the description complexity: the larger model may be able to give a tighter fit. But now model complexity has become exponential in size. Another analogous setting is when say trying to do low rank approximation of matrices. A full rank model will have "lower" error than a lower rank model. In general, it is not clear what you are trying to ask, other than the tautological setup: fewer constraints means lower objective function value....
Apr
22
comment Are the following identities well known?
@mostafa You can see this polarization identity for instance in arxiv.org/pdf/math/0504397.pdf --- it is mentioned in other places too; I don't know the "oldest / canonical" citation for this though; maybe Alexandrov...
Apr
16
comment A conjecture of Blakley and Dixon about odd powers of positive matrices
I'd be quite curious to hear if you discover any extension to Pate's ideas!
Apr
16
comment A conjecture of Blakley and Dixon about odd powers of positive matrices
If $S$ is in addition positive definite, then clearly the conjecture is true. Otherwise, you could try to generalize the proof of T. Pate, and see if holds: ams.org/tran/2012-364-08/S0002-9947-2012-05501-2 (you may also enjoy chasing the references to Sidorenko's conjecture which is much more general than the Blakley-Roy inequality)
Apr
14
comment How do I ensure that my matrix is positive definite?
Using Schur complements we obtain the constraint: $\Sigma \ge P'\Sigma^{-1}P$ which is required for ensuring $M \ge 0$.
Apr
13
answered Largest element in inverse of a positive definite symmetric matrix
Apr
13
comment Moment problem on [-1,1]: necessary and sufficient conditions
Of course, for answering the OP, doing a change of variables to the 1D-case as noted by Robert Israel works!
Apr
13
answered Moment problem on [-1,1]: necessary and sufficient conditions
Apr
11
comment Fast Fourier Transforms for non-trigonometric bases
Did you have a look at stuff like: brown.edu/research/projects/scientific-computing/sites/…
Apr
10
comment A long-lasting conjecture of Pólya & Szegő
Is this conjecture also connected in any way to the Selberg eigenvalue conjecture, or they just happen to share the word "eigenvalue"?
Apr
10
comment SVD when only off-diagonal terms are known
This can be solved as an approximate optimization problem, without truly doing a true SVD.
Apr
6
comment Log-concavity of difference of theta functions
It seems that using the product representation listed here may help: functions.wolfram.com/EllipticFunctions/EllipticTheta3/08
Apr
5
comment Sphere packings : what next after the recent breakthrough of Viazovska (et al.)?
@StanleyYaoXiao Then there would have to be a reason that says why 24 is the final number (perhaps grounded in fixed point theory, no idea)...
Apr
4
comment Examples of high level math that can be motivated to laypeople
You may also benefit from reading some answers to: mathoverflow.net/questions/175847/…
Apr
2
comment Examples of math hoaxes/interesting jokes published on April Fool's day?
I'm voting to close this question as off-topic because it seems to have run its course.