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bio website cse.iitb.ac.in/~aruniyer
location India
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Aug
9
comment Bilinear Optimization Problem
Derivative of a function always lies in the domain of the function. This means that the derivative of your objective has to be a matrix. If you want to translate this into a vector, then rewrite your objective function in terms of the individual matrix components. Then take derivative w.r.t each component.
Aug
9
comment Bilinear Optimization Problem
for the jacobian, note that $||A||_F = trace(A^{T}A)$. Now, use the matrix cookbook [1], to help get the derivatives. [1] lingpipe-blog.com/2011/02/03/the-matrix-cookbook
Aug
9
comment Bilinear Optimization Problem
Note that , if you fix $E^2$(or $C^2$), you can exactly solve for $C^2$(or $E^2$). You can take an iterative approach to solving this. 1. Initialize $E^2$ arbitrarily 2. Solve for $C^2$, say $C^{'}_2$ 3. Set $C^2$ to $C^{'}_2$ 4. Solve for $E^2$, say $E^{'}_2$ 5. Set $E^2$ to $E^{'}_2$ 6. Goto Step 2
Jul
27
comment Compute $ I_{n}=\int_{-\infty}^\infty \frac{1-\cos x \cos 2x \cdots \cos nx}{x^2}\,dx$
A very interesting question with a very beautiful answer.
Jul
14
comment How do you unify probability (Naive Bayes)?
Do you know Naive Bayes? Did you follow the working that the author of the blog shows in his blog post?
Jul
14
awarded  Nice Answer
Jul
12
answered Find Elementary Matrics E1 and E2 such that $E_2E_1$A = I
Jul
7
comment Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$
@AndréNicolas True. This problem is immediate once you see the substitution $y = c\sin(\theta)$. This substitution always comes with a caveat that $|y/c| \leq 1$. Also, one can notice that $\int 1/(y \sqrt{(c^2 + y^2)})dy = -(1/c)acosech(y/c) + C$, this gives an alternative to solve the intermediate integral. So, one has at least a couple of options to solve the intermediate integral (just have to be careful with the gotcha's like the one you pointed out).
Jul
7
answered Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$
Jun
30
answered Introductory (online) texts on Bayesian Network.
Jun
29
revised How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
added 585 characters in body
Jun
29
comment How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
Good catch!! :P
Jun
29
answered How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
Jun
25
comment Integration Example
Above I demonstrate how you nail a toothpick with a big hammer :-D
Jun
25
answered Integration Example
Jun
24
comment An inequality : is it true if it is then how to prove it?
FYI, this is known as Mahler's Inequality
Jun
21
comment A problem in combinatorics
1. Subjects are distinguishable from each other, therefore you need to used ordered counts instead of unordered counts. 2. Once you assign subjects to the third student, you need to also figure out, in how many ways can the remaining subjects be distributed amongst the other three.
Jun
20
answered Find $n$ in $n \log_2 n = c$
Jun
20
answered Calculate: $\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$
Jun
19
answered What is a good book to study linear algebra?