SelisOnelLectureNotes_SolLinearEqII - Solution of Systems...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Solution of Systems of Linear Equations and Applications with MATLAB® : II - Indirect Methods Selis Önel, PhD
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 SelisÖnel© Solution methods for linear systems A x = y Solution of Linear systems I-Direct Methods - Cramer’s Rule -Elimination Methods - Inverse of a matrix - LU Decomposition II-Indirect Methods Iterative Methods
Image of page 2
3 SelisÖnel© Iterative Solution Good for large systems of equations when Gauss elimination is NOT good, i.e., if n>>m for |A m,n ||x n,1 |= |y m,1 | (# unknowns is very large compared to # equations) Simple programming Applicable to nonlinear coefficients Requires an initial guess to start the iteration The goal is to: Choose a good initial guess x0 for x Substitute x0 in the equations and check if the right hand side of equations is equal to the left hand side or if x-x0< ε Increment/decrement x0 until all equations are satisfied
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 SelisÖnel© Iterative Solution Popular technique for finding roots of equations Applied to systems of linear equations to produce accurate results (Generalized fixed point iteration ) Jacobi iteration: Carl Jacobi (1804-1851) Gauss-Seidel iteration: Johann Carl Friedrich Gauss (1777-1855) and Philipp Ludwig von Seidel (1821- 1896)
Image of page 4