CHEN 3201 Lecture Notes - Lecture 2: Linear Algebra
31 Jan 2015
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Starting @ chapter 2 do a bit of linear algebra first then do diff eq. Cramer"s rule: if start w/ 5x5 matrix, then adds to 4 4x4 matrices, then 3 3x3 then 2 2x2etc. work = n! = stirling"s approximation for n = 100, n! Using matlab: takes 0. 227 sec exoflop(2018) = 1018 flop/s. Jewish =~ 104 or 105 years so we want faster way to solve it, even if it might be more approximate but make sure that approximations we make don"t get compounded and propagated by inherent errors in system. Ex: solve just make a small change, but very inconsistent is an ill-conditioned matrix. Norms: gives the size of a vector or matrix. Can specificly tell # rows and columns, but now, more about the magnitude. = max size of system these = 1 norm, 2 norm, and infinity norm. Chen3201_numericalmethods page 1 sum down each column then choose column that has highest sum (transpose of a)
