
Solving Linear Equations using Iterative ImprovementGreg Fee, CECM, SFU
A square system of linear equations with integer coefficients may be represented in matrix form by the matrix equation A.x = b, where A is an n by n matrix of integers, b is a column vector of integers and x is a column vector of unknowns. If the determinant of the matrix A is nonzero, then the solution is unique. An approxiamte solution may found by performing an LU decomposition of the matrix A using floatingpoint arithmetic. If the condition number is small we can find an approximate floatingpoint solution, then we can find a higher precision solution by applying iterative improvement to our current approximation. A modified continuedfraction algorithm can recover the exact rational number solution. 