O(n) Algorithms for Banded Plus Semiseparable Matrices
Jitesh Jain, Hong Li, Cheng‐Kok Koh, V. Balakrishnan · Birkhäuser Basel eBooks · 2010
We present a new representation for the inverse of a matrix that is a sum of a banded matrix and a semiseparable matrix. In particular, we show that under certain conditions, the inverse of a banded plus semiseparable matrix can also be expressed as a banded plus semiseparable matrix. Using this result, we devise a fast algorithm for the solution of linear systems of equations involving such matrices. Numerical results show that the new algorithm competes favorably with existing techniques in terms of computational time.