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
Matrix Computations Setting Up Matrix Problems Matrix Operations Once Again, Setting Up Matrix Problems Recursive Matrix Operations Distributed Memory Matrix Multiplication
Matrix Computations • Setting Up Matrix Problems • Matrix Operations • Once Again, Setting Up Matrix Problems • Recursive Matrix Operations • Distributed Memory Matrix Multiplication
Ax=b Matrix-vector multiplication Matrix- Matrix multiplication Often the amount of work that is required to initialize an n-by-n matrix is as much as the work required to solve forx Fast fourier trans form and fast strassen matrix multiply algorithm
• Matrix-vector multiplication • Matrix- Matrix multiplication • Often the amount of work that is required to initialize an n-by-n matrix is as much as the work required to solve for x • Fast Fourier transform and fast Strassen matrix multiply algorithm Ax=b
Setting up Matrix problems
Setting up Matrix problems
Hilbert matrix A=zeros(n,n) a=zeros(n,n) for i=1: n for i=l,n for i=l: n for j=i:n A(ij=1/(i+j-1); Simple j Recipes A(ij)=1/(i+j-1) AG, D=A(i,j ene end en
Hilbert matrix 1 1 + − = i j aij A=zeros(n,n); for i=1:n for j=1:n A(i,j)=1/(i+j-1); end end A=zeros(n,n); for i=1:n for j=i:n A(i,j)=1/(i+j-1); A(j,i)=A(i,j); end end Simple ij Recipes