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Cholesky

In: Computers and Technology

Submitted By paulsrz111
Words 357
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UNIVERSITY OF SANTO TOMAS
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Faculty of Engineering
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ELECTRONICS ENGINEERING DEPARTMENT
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Second Semester, AY 2014 – 2015

MACHINE PROBLEM

ADVANCED ENGINEERING MATHEMATICS

Submitted by:

MIGUEL AGUILA
CARLO ENRICO LATONIO
MERYL GRACE T. SANTIAGO
PAUL VINCENT C. SUAREZ
3ECE-C

Engr. Krizzy Kanny David
Instructor

April 15, 2015 I. DESCRIPTION

The program is constructed to be able to determine the decomposition of a positive definite square matrix, with eigenvalues that are real and greater than zero using cholesky-decomposition method. For matrix A the formula is A=LLT . The program will have an output of a lower and triangular matrix with elements obtain using the cholesky algorithm. For a 4x4 matrix, A= l110l21l31l41l22l32l42 0 0 0l33l43 0 0l44l11l21000l2200l31 l41 l32l330l42l43l44 .To be able to decompose, the group used the Cholesky algorithm with formulas: l11= a11 , lj1=aj1l11 , lj,j=ajj- k=1j-1lj,k2 and li,j=1lj,j(ai,j-k=1j-1lj,klj,k).

II. CODE

A=input('Enter A: ');

n=sqrt(numel(A)); l(n,n)=1; lt(n,n)=1; for i=1:n for j=1:n P=0; if i==j for k=1:j if k==1 p=A(j,j); else p=-(l(j,k-1)^2); end P=P+p; end l(j,j)=sqrt(P); lt(j,j)=sqrt(P); elseif i>j for k=1:j if k==1 p=A(i,j); else p=-l(i,k-1)*l(j,k-1); end P=P+p; end l(i,j)=P/l(j,j); lt(j,i)=P/l(j,j); else l(i,j)=0; lt(j,i)=0; end end end fprintf('L =\n'); disp(l); fprintf('LT =\n'); disp(lt); The choelsky program works by the

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