The Thomas algorithm is a specialized form of Gaussian elimination for solving a tridiagonal matrix
system. For subdiagonal entries 
, diagonal entries 
, superdiagonal entries 
, and right-hand side 
, set 
and 
. For 
, ..., 
, forward elimination computes
 |
For 
,
..., 
,
it computes
 |
Back substitution starts with 
and continues with 
for 
, ..., 1.
The algorithm requires only linear time and storage in the number of equations. Pivoting or a more general solver may be needed when an elimination denominator vanishes or is too small for stable floating-point computation.
