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:

    ““I have usually found that there was method in his madness.”
    “Some folk might say there was madness in his method.””
    —Sir Arthur Conan Doyle (1859–1930)

    “Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
    —Ralph Waldo Emerson (1803–1882)

    “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)