An Efficient Iteration Method for Toeplitz-Plus-Band Triangular Systems Generated from Fractional Ordinary Differential Equation

Algorithm 1

Forward substitution for lower triangular matrix.

 input: 𝑀,𝐹,𝐴

 output: 𝐹

(1) for    𝑖=1   to   𝑀  by  1 do

(2)   𝑓_𝑖←𝑓_𝑖/𝑎_𝑖,𝑖

(3)   for   𝑗=𝑖+1   to   𝑀  by  1 do

(4)   𝑓_𝑗←𝑓_𝑗−𝑎_𝑖,𝑗𝑓_𝑗