Tridiagonal Matrix Algorithm - Method

Method

The forward sweep consists of modifying the coefficients as follows, denoting the new modified coefficients with primes:

c'_i = \begin{cases} \begin{array}{lcl} \cfrac{c_i}{b_i} & ; & i = 1 \\ \cfrac{c_i}{b_i - c'_{i - 1} a_i} & ; & i = 2, 3, \dots, n-1 \\ \end{array} \end{cases} \,

and:

d'_i = \begin{cases} \begin{array}{lcl} \cfrac{d_i}{b_i} & ; & i = 1 \\ \cfrac{d_i - d'_{i - 1} a_i}{b_i - c'_{i - 1} a_i} & ; & i = 2, 3, \dots, n. \\ \end{array} \end{cases} \,

The solution is then obtained by back substitution:

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