Mathematica's built-in SparseArray function should be used to create tridiagonal matrices.
Mathematica kernel's built-in sparse solver LinearSolve has replaced TridiagonalSolve as a faster solver of tridiagonal matrices.
Suggestion for replacing Tridiagonal
This loads the package in Version 5.2:
This defines the list that will give the nonzero diagonals of a matrix:
Here is the matrix m constructed from the list:
This displays the matrix using MatrixForm:
Mathematica kernel's built-in sparse solver LinearSolve should be used in place of TridiagonalSolve: