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Find solution
if
is tri-diagonal
(maybe after Householder).
With
the system of equations reads
Introducing auxiliary variables and
by the recursive ansatz
we find the
``downward recursion formulae''
Having arrived at and we insert the known values of
in the
``upward recursion formulae''
(The equation for the starting value follows from
and
.)
EXAMPLE:
In
, let
Downward recursion:
,
, and
Upward recursion:
, and
Next: 2.3 Iterative Methods
Up: 2.2 Exact Methods
Previous: 2.2.3 LU Decomposition
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001