copper.hat
Reputation
377/400 score
 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?