Tagged Questions
0
votes
2answers
169 views
Gram-Schmidt method to identify linearly dependent vectors
A method to orthogonalize a set of vectors (vectors of unit length that are mutually orthogonal) is the Gram-Schmidt process:
http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
Note that the ...
4
votes
1answer
62 views
Efficient computation of the extension of a linear basis to completion when the basis is almost complete (ideally using LAPACK routines)
I have a $p \times n$ matrix $B$ (where $n < p$) with orthonormal columns and would like to find a numerically efficient way to extend this matrix to get a complete $p$-dimensional orthonormal ...
5
votes
1answer
128 views
Conjugate Gradient with Hierarchical Basis Functions: How can the hierarchical base be decomposed?
I'm trying to implement a Conjugate Gradient solver using Hierarchical Basis Functions, following this paper.
In section 3 the paper says that the hierarchical basis matrix $S$ can be decomposed into ...
10
votes
1answer
200 views
How can I compute a basis for a matrix Lie algebra given a finite set of generators?
Given an arbitrary set of (numerical) square complex matrices $\mathcal{A}=\{A_1,A_2,\cdots,A_m\}$, I am interested in computing the real matrix Lie algebra generated by $\mathcal{A}$, call it ...
