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LU decomposition

LU decomposition. 日期： 2014/9/30 助教：汪柏岑 授課老師：徐國錦 教授. LU 分解. Doolittle’s method Crout’s method Choleski’s method. Doolittle’s method. library(Matrix ) B=matrix(c(1,2,0,1)) mm <- matrix(c(4,-1,-1,0,-1,4,0,-1,-1,0,4,-1,0,-1,-1,4), nrow =4) lum <- lu (mm) elu <- expand( lum )

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LU decomposition

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  1. LU decomposition 日期：2014/9/30 助教：汪柏岑 授課老師：徐國錦 教授

  2. LU 分解 • Doolittle’s method • Crout’smethod • Choleski’s method

  3. Doolittle’s method

  4. library(Matrix) B=matrix(c(1,2,0,1)) mm <- matrix(c(4,-1,-1,0,-1,4,0,-1,-1,0,4,-1,0,-1,-1,4),nrow=4) lum<- lu(mm) elu <- expand(lum) y=solve(elu$L)%*%B x=solve(elu$U)%*%y elu$L elu$U

  5. Choleski’s method

  6. Exercise 4X4 矩陣 A=matrix(c(4,-1,-1,0,-1,4,0,-1,-1,0,4,-1,0,-1,-1,4),4,4) #定義A矩陣 b=matrix(c(1,2,0,1),4,1) #定義b矩陣 U=chol(A) #使用Choleski's method 算出U L=t(chol(A)) #求U之轉置矩陣L y=solve(L)%*%b #求y矩陣 x=solve(U)%*%y #求x矩陣 L的反矩陣 矩陣相乘 A=LU  Ax=b  Lux=b  Ly=b Ux=y

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