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Parent Chapters-> Omatrix6 linear tridiag

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Solving A Tridiagonal System Of Linear Equations

Syntax	tridiag(a, b, c, d)
See Also	BlockTriDiag , levinson , matrix division

Description
Returns a column vector x, with the same type and dimension as a, that solves the tridiagonal system of linear equations
     a  x    +  b  x   +  c  x     = d    (i = 1, ... , n)
      i  i-1     i  i      i  i+1     i
where n is the number of rows in a. The column vector a is real, double-precision, or complex. The vector b, c, and d have the same type and dimension as a.

For i = 1 the term involving a is not included in the equation above. Similarly, for i = n the term involving c is not included in the equation above. Thus the values of a(1) and c(n) have no effect.

Warning: This method may result in division by 0 unless
     |b | > |a   | + |c   |.
       i      i-1      i+1

Example
     a = {0., .2, .5}
     b = {1., 1., 1.}
     c = {.5, .2, .0}
     d = {2., 3., 5.}
     x = tridiag(a, b, c, d)
     print x
returns
     {
     1
     2
     4
     }
If you continue by entering
     i = 2
     a(i) * x(i - 1) + b(i) * x(i) + c(i) * x(i + 1)
O-Matrix will respond
     3