Faster inverse of a lower triangular matrix than inv(A)?

Dear All,

I have a sparse lower triangular matrix A. I want to obtain the inverse of A. A has a size of 6000 X 6000. I find inv(A) takes more than 5 seconds. I do not know if there is a faster approach to get the inverse of A?

Thanks. Bei

Answer 1

[Matt J]

The reason I want to obtain the inverse of A is that I need to select a number of rows from inv(A) for further uses. I do not just solve Ax=b linear equation.

The two are almost the same thing:

 B=speye(size(A));

 rows = B(rowIndices,:)/A

[Benson Gou]

Thanks a lot, Matt. It works very well. 0.0549 second.

Bei

Answer 2

[Torsten]

See here

https://de.mathworks.com/matlabcentral/answers/332233-updating-inverse-of-a-lower-triangular-matrix

why it is a bad idea to invert a lower triangular matrix.

[Benson Gou]

Thanks, Torsten.

The reason I want to obtain the inverse of A is that I need to select a number of rows from inv(A) for further uses. I do not just solve Ax=b linear equation.

I also used the idea of x=A\b to obtain the rows (800 rows) I want to select from inv(A). But it took more than 9 seconds.

Thank you, anyway.