Thomas Algorithm

Updated 01 Oct 2026

•
What it is
- •
  a specialized elimination and back-substitution algorithm for tradiagonal linear systems
•
Efficiency
- •
  uses $O(n)$ work and storage because only the three diagonals are needed
•
Limitations
- •
  the ordinary algorithm does not pivot and requires its generated pivots to remain nonzero
- •
  favorable matrix properties, such as suitable diagonal dominance or positive definiteness, support reliable use
•
Related
- •
  Cubic Spline Interpolation
- •
  Sparse Matrix

Linked references 3