complexity {spam} | R Documentation

## Complexity for Sparse Matrices

### Description

A few results of computational complexities for selected sparse algoritms in `spam`

### Details

A Cholesky factorization of an n-matrix requires n^3/3 flops. In case of banded matrices (bandwidth p, p<<n) a factorization requires about 2np^2 flops. Forward- and backsolves for banded matrices require essentially 2np flops.

George and Liu (1981) proves that any reordering would require at least O(n^3/2) flops for the factorization and produce at least O(n log(n)) fill-ins for square lattices with a local neighbor hood.
They also show that algorithms based on nested dissection are optimal in the order of magnitude sense.

More to follow.

### References

George, A. and Liu, J. (1981) Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall.

### See Also

`det`, `solve`, `forwardsolve`, `backsolve` and `ordering`.

[Package spam version 2.2-2 Index]