Tagged Questions
3
votes
2answers
143 views
Is the QR algorithm for computing eigenvalues efficient for today's standards?
I was looking at the QR factorization algorithm of a matrix to approach eigenvalues. At the Wikipedia page they state that it was developed in the 50's and took over the LR algorithm. They also state ...
1
vote
0answers
34 views
Algorithms for Performing Large Integer Matrix Operations w/ Numerical Stability
I'm looking for a library that performs matrix operations on large sparse matrices w/o sacrificing numerical stability. Matrices will be 1000+ by 1000+ and values of the matrix will be between 0 and ...
7
votes
1answer
419 views
What would be a good method for finding the submatrix with the largest sum?
This question is from an ongoing contest which ends in 4 days. It is this problem from the October Challenge.
Given:A Matrix (Not necessarily square) filled with negative and positive ...
0
votes
0answers
135 views
Computational cost for Gauß Seidel and Jacobi algorithm
What is the computational cost of the Gauß-Seidel and the Jacobi algorithms (as presented on Wikipedia: http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method and ...
2
votes
2answers
254 views
Fast algorithm for LU factorization
If A is a symmetric matrix, is there a fast algorithm for LU factorization? I know this algorithm for non-symmetric matrix.
...
0
votes
0answers
39 views
Zoom progression not linear
I have an algorithm for the editing of an image. There is an image and a rectangle that is smaller than the image (e.g. 3/4 of it) and that represents a section of the image. This section has to be ...
0
votes
0answers
21 views
Elements of sparse matrix products
Following Problem:
I have to calculate a sum
$$
\sum_{k1,k2,k3,k4,k5} Mat1[k5,k1]*Mat2[k1,k2]*Mat3[k2,k3]*Mat4[k3,k4]*Mat5[k4,k5] * SomeFunction[k1,k2,k3,k4,k5]
$$
Mat1,..,Mat5 are large matrices ...
0
votes
1answer
272 views
calculating matrix rank with gaussian elimination
[The answer to my problem has been found: it was a simple sign error. the pseudo code below is fine]
I have implemented an algorithm in c++ that should calculate the matrix rank of a given n x m ...
2
votes
1answer
212 views
Confusion with “trivial Givens rotations” being used to eliminate values in a vector
I am currently studying the QR algorithm described in Computing the eigenvalues of a
companion matrix and have come to something that has me scratching my head. I'm trying to work this method out on ...
1
vote
0answers
105 views
The fastest algorithm of computing Principal eigenvector of a non-negative-entries matrix
I am studying the QR algorithm, is it the fastest one in this situation?
2
votes
1answer
76 views
Fast Algorithm For Adding An Equation To A System?
Assume an $N \times N$ matrix $A$ and a length $N$ vector $b$. I've already solved the system $Ax = b$ for $x$ using standard methods. (If you want you can assume that I have the inverse of $A$ as ...
2
votes
0answers
330 views
QR with column pivoting
Golub and van Loan's algorithm 5.4.1
for QR factorization is suitable as a rank revealing algorithm.
The results are R, Q with the subdiagonal elements stored in "factored form" and the column ...
3
votes
1answer
164 views
Finding SVD efficiently for $AB^T$
I posted this on cs theory yesterday but did not get an answer and hence I am posting here.
I have a low rank matrix given as $AB^T$ where $A,B \in \mathbb{R}^{n \times p}$ and $p \ll n$. (I know $A$ ...
