Register to reply

The inverse of a banded matrix

by S_David
Tags: banded, inverse, matrix
Share this thread:
S_David
#1
Jun12-14, 05:52 PM
P: 601
Hello all,

I have say 512-by-512 matrix, but based on the structure of this matrix most elements not on the diagonals between -5 to +5 (- stand for diagonal below the main diagonal, and + for diagonal above the main diagonal) are small relative to the elements of the mentioned diagonals. So, I create a 512-by-512 banded matrix, where I null all other elements not on the mentioned diagonals.

Now the question is: will there be a huge complexity saving if I want the inverse of the matrix by inverting its banded version instead of the original matrix?

Thanks
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
AlephZero
#2
Jun12-14, 07:12 PM
Engineering
Sci Advisor
HW Helper
Thanks
P: 7,177
In computer calculations, "inverting a matrix" is almost always the wrong thing to do, even if you have a nice looking math equation with an inverse matrix in it.

In this case there will be a huge "complexity" increase, because the inverse matrix will be fully populated, not banded.

What you really want to do is probably solve a set of equations or something similar. If you decompose your banded matrix as A = LDU or something similar, where L and U are lower and upper triangular and have the same bandwidth as A, you preserve the efficiency by not needing to process all the zero terms in L and U.
S_David
#3
Jun21-14, 04:01 PM
P: 601
Quote Quote by AlephZero View Post
In computer calculations, "inverting a matrix" is almost always the wrong thing to do, even if you have a nice looking math equation with an inverse matrix in it.

In this case there will be a huge "complexity" increase, because the inverse matrix will be fully populated, not banded.

What you really want to do is probably solve a set of equations or something similar. If you decompose your banded matrix as A = LDU or something similar, where L and U are lower and upper triangular and have the same bandwidth as A, you preserve the efficiency by not needing to process all the zero terms in L and U.
Could you please tell me more about this process?


Register to reply

Related Discussions
Matlab - Banded Matrix Engineering, Comp Sci, & Technology Homework 1
Closed-form determinant of a hermitian banded toeplitz matrix! Linear & Abstract Algebra 0
Matrix Theory (Matrix Inverse test question) Calculus & Beyond Homework 1
Lineal Algebra: Inverse Matrix of Symmetric Matrix Calculus & Beyond Homework 7
Matrix pseudo-inverse to do inverse discrete fourier transform Linear & Abstract Algebra 3