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Results tagged with linear-algebra
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user 164
Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.
0
votes
2
answers
983
views
Finding matrix form of Ellipsoid given general form
I have data that I would like to fit with an ellipsoid and I am currently fitting it via the following Matlab commands:
xs = pts(:,1);
ys = pts(:,2);
zs = pts(:,3);
A0 = [xs.^2 ys.^2 zs.^2 xs.*ys ys …
- 2,159
3
votes
2
answers
978
views
Linear regression via SVD not producing best fit with escalating polynomial degree
I am using a basic singular value decomposition (via LAPACK) routine in FORTRAN to solve an overdetermined system in the form of $A\cdot X = B$ where $\mathrm{size}(A) = [m,n]$ with $m > n$.
My sampl …
- 2,159
4
votes
Can the solution of a linear system of equations be approximated for only the first few vari...
The long answer is...sort of.
You can re-arrange your system of equations such that the farthest right $k$ columns are the variables which you wish to solve for.
Step 1: Perform Gaussian Elimination …
- 2,159
4
votes
1
answer
99
views
Does the covariance matrix in Least Squares depend upon the input data?
I had always assumed that the covariance matrix depends upon the amount and quality of your input data, but I am finding out that this is not the case. Is this true?
We want to fit $f(t) = \Sigma_{i= …
- 2,159
0
votes
1
answer
105
views
Most efficient way to compute eigenvectors / values of this matrix?
I have a symmetric $ 3 \times 3 $ matrix $A$ and I need to compute the eigenvectors and eigenvalues of this. I know that I can use something like Lapack, but I also know that this can be computed anal …
- 2,159
1
vote
1
answer
1k
views
Constrained linear least squares matrix equation
It has been a while since I have done linear least squares, so forgive the simple question, but here goes:
I am attempting to find the best fit coefficients, $\{c_i\}$, of a linear combination of bas …
- 2,159
9
votes
3
answers
1k
views
What should be the criteria for accepting/rejecting singular values?
I am solving a system using singular value decomposition. The singular values (before scaling) are:
1.82277e+29
1.95011e+27
1.15033e+23
1.45291e+21
4.79336e+17
7.48116e+15
8.31087e+12
1.71838e+11
5.6 …
- 2,159