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:

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

    “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)

    “The most passionate, consistent, extreme and implacable enemy of the Enlightenment and ... all forms of rationalism ... was Johann Georg Hamann. His influence, direct and indirect, upon the romantic revolt against universalism and scientific method ... was considerable and perhaps crucial.”
    —Isaiah Berlin (b. 1909)