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Apr
9
awarded  Popular Question
Mar
30
comment Linear regression of time series data - moving linear regression
I don't know if this can be done in a simple way, but as a start I'd note that least-square fitting is done by calculating the inverse of a matrix of the form $A^TA$ where $A$ is a matrix constructed from the observations. Updating the inverse in each incremental step might be done via the Sherman-Morrison formula
Mar
30
comment Linear regression of time series data - moving linear regression
Why not use weights, that decrease (say, exponentially), the further you go into the past? That is, use a standard linear regression with weights $w_i=e^{-\lambda i}$ where $w_i$ is the weight of the $i$-th measurement, and the most recent measurement is $i=1$. $\lambda$ is a parameter that determines how much you want to bias your estimate towards more recent data.
Mar
29
comment Minimal distance between points on two graphs
Nice question. I don't have time to solve it now, but I think that defining the distance function as $$f(x,y)=(x-y)^2+(\sin(x)+2-\sin(y))^2$$ and moving to the variables $$x'=x-y,\qquad y'=x+y$$ might greatly simplify things.
Mar
8
accepted When is the inverse of a sparse matrix dense?
Feb
12
asked When is the inverse of a sparse matrix dense?
Feb
4
comment Symmetric gram matrix and orthogonality
By definition (for symmetric matrices) they are orthogonal if and only if $A^TA=I$.
Feb
1
revised There is relation that is symmetric and transitive but not reflexive?
added 8 characters in body
Feb
1
comment There is relation that is symmetric and transitive but not reflexive?
OK. I still think it's a matter of taste, but I'll edit my answer.
Feb
1
comment There is relation that is symmetric and transitive but not reflexive?
That's a matter of taste. If you assume that $y$ exists and that $y=x$ then it's like assuming reflexivity in the first place, which is kind of cheating.
Feb
1
answered There is relation that is symmetric and transitive but not reflexive?
Dec
25
comment Which of the following conditions must necessarily be true?
You mean mutually exclusive conditions?
Dec
15
awarded  Yearling
Dec
9
awarded  Caucus
Nov
26
awarded  Civic Duty
Nov
15
comment Is this polynomial irreducible in $\mathbb F_2[X]$
I agree. "Yes" is a solution to the above question.
Nov
15
comment Is this polynomial irreducible in $\mathbb F_2[X]$
wolframalpha.com/input/…
Nov
15
comment Is this polynomial irreducible in $\mathbb F_2[X]$
$$\left(x^8+x^5+x^4+x^3+1\right) \left(x^8+x^7+x^6+x^4+x^2+x+1\right)$$
Oct
23
comment Find $x$ for which the rank is as minimal/maximal as possible
Hint: The first and second rows are indepedent. So for all $x$, the rank is $\ge2$. There are only three rows, so the rank is $\le3$. There're not so many options...
Oct
19
answered How to show that the curve $ (x,y,z) = \langle \cos t, \sin t, c\sin t\rangle $ is an ellipse?