Sparse matrix factorization

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Bhumi Patel

Implementation of Sparse matrix factorization using sequential and parallel algorithms.

Engineering

The Multifrontal Algorithm for Sparse
Matrix Factorization

The extend-add operation on two 3*3 triangular
matrices. It is assumed that i0 < i1 < i2 < i3.
Example

(b) Update matrices after one step of elimination in
each frontal matrix

(c) Frontal matrices at the second level of the
elimination tree

(d) Update matrices after elimination of nodes 2, 5, 11,
and 14

(e) Factorization of the remainder of the matrix

(a) Update matrices before the first parallel extend-add
operation

(b) Update matrices after the first parallel extend-add
operation

(c) Update matrices before the second parallel extend-
add operation

(d) Update matrices after the second parallel extend-
add operation

(e) Update matrices before the third parallel extend-
add operation

(f) Update matrices after the third parallel extend-add
operation

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Sparse matrix factorization

1. Sparse Matrix Factorization

7. The Multifrontal Algorithm for Sparse Matrix Factorization

8. Sequential Algorithm

10. The extend-add operation on two 3*3 triangular matrices. It is assumed that i0 < i1 < i2 < i3. Example

11.

12. (a) Initial frontal matrices

13. (b) Update matrices after one step of elimination in each frontal matrix

14. (c) Frontal matrices at the second level of the elimination tree

15. (d) Update matrices after elimination of nodes 2, 5, 11, and 14

16. (e) Factorization of the remainder of the matrix

17. Parallel Algorithm Partition :

18.

19.

20. (a) Update matrices before the first parallel extend-add operation

21. (b) Update matrices after the first parallel extend-add operation

22. (c) Update matrices before the second parallel extend- add operation

23. (d) Update matrices after the second parallel extend- add operation

24. (e) Update matrices before the third parallel extend- add operation

25. (f) Update matrices after the third parallel extend-add operation

26. Thank You.

Sparse matrix factorization

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