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Sparse Matrix inversion without actual inversion

I want to know what are the efficient way to invert a Sparse Matrix? Are there any algorithm,linear algebra or expansions that make this task easier with out actually inverting the matrix? Thank you ...
3
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1answer
272 views

Need clarification about the use of Big-O to describe matrix sparsity

In one of my courses, Big-O notation was used for defining what a sparse matrix is, under the context of qualifying for suitability for a particular set of linear algebra algorithms. I looked around ...
3
votes
1answer
709 views

Finding the bandwidth of a band matrix

I am designing an algorithm that solves a linear system using the QR factorization, and the matrices I am dealing with are sparse and very large ($6000 \times 6000$). In order to improve the ...
0
votes
1answer
624 views

Running time of sparse matrix multiplication

Given a sparse matrix $M \in \mathbb{R}^{n \times m}$ with $n \ll m$ and $\mathsf{nnz}$ being the number of non-zero-components. What is the running time of computing $M M^T$?
2
votes
1answer
260 views

Permutation on matrix to fill main diagonal with non-zero values

I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal is filled ...