A new algorithm with its scilab implementation for solution of bordered tridiagonal linear equations

An approach is presented to solve bordered tridiagonal linear equations (BTLES). By the approach, a BTLE is first converted into three or more tridiagonal linear equations (TLES) that are independent each other, then the solution of the BTLE can be obtained via the solutions of the TLES. Since the TLES are independent each other, their solution can be obtained via parallel computing under heterogeneous environments. The approach costs at most O(n
²
) of time complexity in sequential mode. Detail mathematical deduction is presented to reveal the approach and a framework is introduced to implement the approach. The approach, which can also be available for grid computing, greatly increases the flexibility and agility of computations as well as the computational efficiency.