CHEN 3201 Lecture Notes - Lecture 13: Pivot Element, Gaussian Elimination, Royal Institute Of Technology
22 Feb 2015
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Gaussian elimination (correcting last lecture) i=k+1:n j=k+1:n stay the same we know they should be 0. Program that"s in the book function x = linear_ngaussel(a,b) %called naive gaussian elimination b/c just assumed it would work for everything. Problems when the diagonal entries (called pivots) are small. -but when they are really small, there can be round-off errors partial pivoting. In the kth elimination step, search in the kth column for the largest entry. If there is a larger entry, swap the rows but this has problems too. Key problem: all entries at the diagonal and below = 0. -> full pivoting (search all columns and rows and swap) using gaussian elimination for determinants. Recall: cramer"s rule is n! (n3 is less than n!, so we"re good) 2)keep track of # of pivots when initiallizing a sum, do it w/ 0 when initializing product, initialize w/ 1 every exam has program.
