backward substitutionの例文

例文

1. A first sweep eliminates the a _ i's, and then an ( abbreviated ) backward substitution produces the solution.
2. Solving it in turn reduces the next last equation to one unknown, so that this backward substitution can be used to find all of the unknowns:
3. Considering this system, the elimination algorithm and backwards substitution using four-digit arithmetic yield the correct values x 1 = 10.00 and x 2 = 1.000.
4. Note that in both cases we are dealing with triangular matrices ( " L " and " U " ) which can be solved directly by forward and backward substitution without using the Gaussian elimination process ( however we do need this process or equivalent to compute the " LU " decomposition itself ).