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Feb
18
comment Why does Newton's Method Diverge when f''(r)=0 or r is an inflection point?
It doesn't? Newton's method has no trouble solving $f(x)=x$. Maybe you're thinking of Newton's method for optimization instead of Newton's method for solving equations?
Feb
17
comment A circle can include all but one of n points, but which one can it be?
The second hypothesis follows from the fact that a disk covering $n-1$ points is a superset of their convex hull.
Feb
17
comment What are some examples where it is analytically easier to compute integrals than derivatives?
"I have read in many places..." Can you cite some of these places for more context?
Feb
17
comment Intuition behind the “infinite velocity” of a falling ladder
One could imagine that the end of the ladder is on frictionless wheels that run on rails attached to the wall, and the rails enclose the wheels on both sides. Then one can see that when the ladder is nearly horizontal, it becomes extremely difficult to pull the other end at a constant velocity, because the rails are pulling back equally hard...
Feb
17
comment Intuition behind the “infinite velocity” of a falling ladder
The ladder will detach from the wall well before that happens. The velocity only approaches infinity if the end of the ladder is forced to remain in contact with the wall all the way down.
Feb
17
comment Can I just make this function up?
One could argue that the function already exists, you would merely be picking it out and giving it a name. (There are actually several choices of the function depending on which branches you choose, but any such choice still "exists" in a Platonic sense.)
Feb
16
comment What is the order of convergence of a vector?
The order of convergence of a vector is defined to be the order of convergence of its norm. In this case the norm is approximately $1/k$ for large $k$.
Feb
14
comment Differentiation as Rotation
"Is it possible to say that the the differential operator is diagonalised in the Fourier domain?" Yes. "Is the differential operator the equivalent of the rotation matrix in finite dimensional matrices?" No. Diagonal matrices and rotation matrices are different.
Feb
13
comment Turn off the ovens! An optimization problem
How well do Baron and Couenne scale on larger problems? Are there guarantees on finding the global minimum? (I presume the answers to both these questions can't be favourable.)
Feb
13
comment Conditions for convex hulls
Given a finite set of points in an affine space, their convex hull always exists.
Feb
12
comment convex optimization with multiple nonsmooth terms
Minimize $\underbrace{f(x)}_{\text{first function}}+\underbrace{g(z_1)+h(z_2)}_{\text{second function}}$ subject to $\begin{bmatrix}x\\x\end{bmatrix}=\begin{bmatrix}z_1\\z_2\end{bmatrix}$.
Feb
12
comment convex optimization with multiple nonsmooth terms
ADMM will work.
Feb
11
comment What is $\left | \left | A \right | \right |$ equals to in linear algebra?
Um, what are you trying to say with your comments?
Feb
10
comment Explain “homotopy” to me
@Asaf: I think it becomes a neat distillation of the StackExchange model -- in appearance we explain things to "the asker", but really we explain them to all the other people who might read our answers in the future.
Feb
10
comment What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)
Surely you already know what a rounded rectangle looks like.
Feb
10
revised What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)
added 86 characters in body
Feb
10
revised What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)
added 90 characters in body
Feb
10
answered What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)
Feb
9
awarded  Nice Answer
Feb
9
comment Can covariance (X,Y) be easily expressed in term of Var(X), Var(Y), E(X), and E(Y)?
Consider (i) $X$ and $Y$ are i.i.d. standard normal, (ii) $X$ is standard normal and $Y=X$. Both cases have the same $E(X)$, $E(Y)$, $\operatorname{Var}(X)$, $\operatorname{Var}(Y)$ but different $\operatorname{Cov}(X,Y)$.