MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering IFall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.MATLAB’s backslash command to solve Ax = b � x=A\b for dense A performs these steps (stopping when successful): 1. If A is upper or lower triangular, solve by back/forward substitution 2. If A is permutation of triangular matrix, solve by permuted back substitution (useful for [L,U]=lu(A) since L is permuted) 3. If A is symmetric/hermitian • Check if all diagonal elements are positive • Try Cholesky, if successful solve by back substitutions 4. If A is Hessenberg (upper triangular plus one subdiagonal), reduce to upper tri-angular then solve by back substitution 5. If A is square, factorize P A = LU and solve by back substitutions 6. If A is not square, run Householder QR, solve least squares problem Mathworks documentation:
View Full Document
Unlocking...