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:

    “The insidiousness of science lies in its claim to be not a subject, but a method. You could ignore a subject; no subject is all-inclusive. But a method can plausibly be applied to anything within the field of consciousness.”
    —Katharine Fullerton Gerould (1879–1944)

    “I do not know a method of drawing up an indictment against a whole people.”
    —Edmund Burke (1729–1797)

    “The method of painting is the natural growth out of a need. I want to express my feelings rather than illustrate them. Technique is just a means of arriving at a statement.... I can control the flow of paint: there is no accident, just as there is no beginning and no end.”
    —Jackson Pollock (1912–1956)