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11m
comment Multistep Method: Gear's Formula Interpolation
Something like $q(t) = y_{n-1} {(t-t_{n})(t-t_{n+1}) \over (t_{n-1}-t_{n})(t_{n-1}-t_{n+1}) } + \cdots $.
6h
comment Multistep Method: Gear's Formula Interpolation
You need a quadratic polynomial that passes through the three points $(t_i, y_i)$ with $i=n-1,n,n+2$.
6h
comment Multistep Method: Gear's Formula Interpolation
The instructions given above are fairly explicit. Write a formula for the polynomial $q$ given the data points $(t_i,y_i)$. Compute $q'(t_{n+1})$. Remember that there is a constant step size, so $t_{i+1}-t_i = h$.
9h
comment How do I link dimension of a normed vector space with closedness?
$W$ is closed regardless of dimension because translation and $x \mapsto \|x\|$ are continuous and $[0,r]$ is closed.
9h
comment How do I link dimension of a normed vector space with closedness?
What is $W$? ${}{}{}$
10h
comment Uniform unboundedness of linear operators
@MatthewKvalheim: I have had my intuition thwarted so many times that I would say you need to split your time between looking and trying to prove!
10h
comment Uniform unboundedness of linear operators
@DanielFischer: Almost certainly!
10h
comment Uniform unboundedness of linear operators
@DanielFischer: That's funny, I am usually the slowest!
10h
answered Uniform unboundedness of linear operators
11h
comment If a subset of metric space $(X,d)$ like $S$ is closed and bounded, does it imply that $X$ is totally bounded?
@BrianM.Scott: I often feel that the discrete metric is cheating :-).
12h
comment If the integral of $|f_n|$ converges to zero, so does the integral of $f_ng$ for integrable $g$
What does the $0$ on $C_{cpt}^0$ mean?
12h
comment If the integral of $|f_n|$ converges to zero, so does the integral of $f_ng$ for integrable $g$
For (b), note that the compactly supported continuous functions are dense in $L^1$.
13h
comment Normal modes energy terms
This would probably get better answers on the Physics SE.
13h
answered If a subset of metric space $(X,d)$ like $S$ is closed and bounded, does it imply that $X$ is totally bounded?
14h
comment How to combine inequalities
Draw a picture.
15h
comment Initial value problem $y'=e^{-y^{2}}-1.$
If there is a solution defined on the real line and $f$ is locally Lipschitz, then the solution is unique.
1d
comment How to identify an orthogonal(orthonormal matrix)?
Vectors are orthogonal if their inner product is zero.
1d
comment How to identify an orthogonal(orthonormal matrix)?
Well, you could notice that the columns (or rows) are orthogonal and that the columns have unit length. This is equivalent to computing the product...
1d
comment How to identify an orthogonal(orthonormal matrix)?
Note that $A^n = \begin{bmatrix} 1 & n \\ 0 & 1 \end{bmatrix}$. Also note that $P^T Q^{2005} P = P^T A^{2005} P$.
1d
comment Isometric embedding of $\ell ^ 1$ in $\ell ^\infty$ in finite dimensions
What do you mean by embedded?