MAT223H1 Chapter Notes - Chapter 1.3: Roundoff, Pivot Element, Golu
Document Summary
Elimination methods work ne for small systems, but can lead to errors when implemented on computer system due to round-off errors. In addition, the number of operations required to per- form during the elimination algorithm grows polynomi- ally with the number of equations/unknowns. Our goal is to show a few alternatives to standard elimina- tion methods. When the system is not too large, the round-off error can be negligible, but if the system is large that error can be- come signi cant. One way to control round-off error is using partial pivot- ing. The idea behind partial pivoting is to select the largest leading entry - in terms of absolute value - for the pivot position before starting the elimination process. Consider the linear system a11x1 + a12x2 + . + a1nxn = b1 a21x1 + a22x2 + . + a2nxn = b2 an1x1 + an2x2 + . The jacobi algorithm for solving a linear system has the following steps.
