复旦大学：《Matlab》（ppt实验英文版）Chapter 7 The QR and Cholesky Factorizations

Introduction to scientific Computing A Matrix Vector Approach Using Matlab Written by Charles FVan Loan 陈文斌 Wbchen(fudan. edu. cn 复日大学

Introduction to Scientific Computing -- A Matrix Vector Approach Using Matlab Written by Charles F.Van Loan 陈 文 斌 Wbchen@fudan.edu.cn 复旦大学

Chapter 7 The qr and cholesky Factorizations Least Squares Fitting The qr factorization The cholesky factorization High-Performance Cholesky

Chapter 7 The QR and Cholesky Factorizations • Least Squares Fitting • The QR factorization • The Cholesky Factorization • High-Performance Cholesky

Least Squares Fitting 0 overdetermined 34‖x1 56 Given A∈R""andb∈R",fndx∈Rnto minimize Ax-61

Least Squares Fitting             =           1 1 0 5 6 3 4 1 2 1 2 x x 2 minimize Given and , find to Ax b A R b R x R m n m n −     overdetermined

Setting Up Least Squares Problems x∈[25,】 ,(1)=∑(a+k)-x n、(a,B) B

Setting Up Least Squares Problems f (x) = x, x[.25,1]   = = + − m i m i i x x 1 2  (, ) (  ) 2 2 2 1 2 1 1 1 1 ( , )             −                  = m m m f f f x x x        

Matlabs Least Squares Tools XLSAb m=2,apha=0.33333,bea=0.666667 m=100,apha=0.369810,bea=0.652299 0 0.5 0.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 m = 100, alpha = 0.369810, beta = 0.652299 Matlab’s Least Squares Tools xLs=A\b; 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 m = 2, alpha = 0.333333, beta = 0.666667