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:

Read more about this topic:  Tridiagonal Matrix Algorithm

Famous quotes containing the word method:

    “You know, I have a method all my own. If you’ll notice, the coat came first, then the tie, then the shirt. Now, according to Hoyle, after that the pants should be next. There’s where I’m different. I go for the shoes next. First the right, then the left. After that, it’s every man for himself.”
    —Robert Riskin (1897–1955)

    “There is no method but to be very intelligent.”
    —T.S. (Thomas Stearns)

    “Argument is conclusive ... but ... it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.... For if any man who never saw fire proved by satisfactory arguments that fire burns ... his hearer’s mind would never be satisfied, nor would he avoid the fire until he put his hand in it ... that he might learn by experiment what argument taught.”
    —Roger Bacon (c. 1214–1294)