Editing Tridiagonal matrix (section)

===Determinant===
{{Main|Continuant (mathematics)}}
The [[determinant]] of a tridiagonal matrix ''A'' of order ''n'' can be computed from a three-term [[recurrence relation]].<ref>{{Cite journal | last1 = El-Mikkawy | first1 = M. E. A. | title = On the inverse of a general tridiagonal matrix | doi = 10.1016/S0096-3003(03)00298-4 | journal = Applied Mathematics and Computation | volume = 150 | issue = 3 | pages = 669–679 | year = 2004 }}</ref> Write ''f''<sub>1</sub>&nbsp;=&nbsp;|''a''<sub>1</sub>|&nbsp;=&nbsp;''a''<sub>1</sub> (i.e., ''f''<sub>1</sub> is the determinant of the 1 by 1 matrix consisting only of ''a''<sub>1</sub>), and let

:<math>f_n = \begin{vmatrix}
a_1 & b_1 \\
c_1 & a_2 & b_2 \\
& c_2 & \ddots & \ddots \\
& & \ddots & \ddots & b_{n-1} \\
& & & c_{n-1} & a_n
\end{vmatrix}.</math>

The sequence (''f''<sub>''i''</sub>) is called the [[continuant (mathematics)|continuant]] and satisfies the recurrence relation

:<math>f_n = a_n f_{n-1} - c_{n-1}b_{n-1}f_{n-2}</math>

with initial values ''f''<sub>0</sub>&nbsp;=&nbsp;1 and ''f''<sub>−1</sub>&nbsp;=&nbsp;0. The cost of computing the determinant of a tridiagonal matrix using this formula is linear in ''n'', while the cost is cubic for a general matrix.