The Forward Substitution Method is a direct algorithmic procedure used to solve lower triangular systems of linear equations in numerical analysis and computational mathematics. It relies on the mathematical property that, given a lower triangular matrix with non-zero diagonal entries, each variable can be sequentially determined by substituting previously calculated values into rows above it. This mechanism constitutes an essential component of decomposed system solvers, specifically functioning as the forward phase required before backward substitution in larger linear algebraic workflows.
Solves a lower-triangular linear system top-down by forward substitution, solving for each variable in turn.