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Systems of Linear Equations on MATLAB-Machine Learning-Lecture Handout

Lecture Notes, Machine Learning

Post: July 19th, 2012
Description
This lecture notes was distributed for Machine Learning course by Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS). Its main points are: Systems, Linear, Equations, MATLAB, Implementation, Residuals, Elementary, Elimination, Matrices, Gaussian
This lecture notes was distributed for Machine Learning course by Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS). Its main points are: Systems, Linear, Equations, MATLAB, Implementation, Residuals, Elementary, Elimination, Matrices, Gaussian
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Contents
Lecture Outline (1/2)       Calculating Small Residuals Forward-substitution for lower triangular system Lx = b Back-substitution for upper triangular system Ux = b Elementary Elimination Matrices Gaussian Elimination Finding Permutation Matrix Dr. Hanif Durad 2 Lecture Outline (2/2)      Gaussian Elimination with Partial Pivoting Gaussian Jordan Elimination with Partial Pivoting Crout’s Decomposition Cholesky’s Decomposition Tridiagonal Decomposition Dr. Hanif Durad 3 Example 2.8 :Calculating Small Residuals A=[.913 .659;.457 .33] A= 0.9130 0.6590 0.4570 0.3300 >> b=[.254 .127]' b= 0.2540 0.1270 Refer EMSE, P-230 >> x=A\b x= 1.0000 -1.0000 >> r=A*x-b r= 1.0e-016 * 0 -0.5551 >>cond(A) ans = 1.2485e+004 P-63 Forward-substitution for lower triangular system Lx = b >> L L= -1 0 -4 -6 12 >> b b= 1 -6 3 >> x=LTriSol(L,b) x= -1.0000 1.6667 0.3333 0 0 2 P-65 Refer SCMV, P-198 Back-substitution for upper triangular system Ux = b >> U U= 122..

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