Timeline for some problem about the discrete of the first derivative operator
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 5 at 18:57 | history | edited | kjetil b halvorsen | CC BY-SA 4.0 |
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| Mar 5 at 18:44 | comment | added | Andreas Blass | There seems to be a typo in the second row of matrix $D$. The diagonal entry should be $1$ and the other entry shjoould be $-1$. With this correction, I agree with @CarloBeenakker's first comment that the matrices differ only by an overall minus sign, which makes no difference. | |
| Mar 5 at 12:49 | review | Close votes | |||
| Mar 22 at 3:10 | |||||
| Mar 5 at 12:33 | comment | added | bing | @Carlo Beenakker, Thanks for your time, the result i got with matlab has the same real part with your result. Maybe the imaginary parts i got is due to some numerical error, as one of the eigenvalue of (L'*L) is nearly zero. Thank you so much. | |
| Mar 5 at 12:31 | comment | added | Carlo Beenakker | this is the square root in your case: $\left( \begin{array}{cccc} 1 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 1 \\ \end{array} \right)^{1/2}=\left( \begin{array}{cccc} 0.815493 & -0.544895 & -0.162212 & -0.108386 \\ -0.544895 & 1.19818 & -0.49107 & -0.162212 \\ -0.162212 & -0.49107 & 1.19818 & -0.544895 \\ -0.108386 & -0.162212 & -0.544895 & 0.815493 \\ \end{array} \right)$ | |
| Mar 5 at 12:18 | comment | added | bing | @Carlo Beenakker ,Thanks for your comment. I create a matrix in matlab first with L=[1 -1 0 0;0 1 -1 0;0 0 1 -1] . Then I use the command sqrtm(L'*L) and got a complex matrix but the imaginary parts of all the complex numbers are very small, maybe it's due to some numerical error? | |
| Mar 5 at 12:07 | comment | added | Carlo Beenakker | your matrices $D$ and $L_1$ only differ by a minus sign; since $B=(D^\top D)^{1/2}$ the minus sign is irrelevant; the matrix $D^\top D$ is positive definite, so it has a real square root, you are probably making a mistake if you get an imaginary answer. | |
| S Mar 5 at 11:53 | review | First questions | |||
| Mar 5 at 18:57 | |||||
| S Mar 5 at 11:53 | history | asked | bing | CC BY-SA 4.0 |