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Inverse Power Method Lab Report
1. PRACTICAL
Name- Saloni Singhal
M.Sc. (Statistics) II-Sem.
Roll No: 2046398
Course- MATH-409 L
Numerical Analysis Lab
Submitted To: Dr. S.C. Pandey
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2. OBJECTIVE
1. Create an M-file to implement
Inverse Power Method to find least
eigen value.
1. Write the program to find the
convergence.
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3. Theory
The inverse power method is an iterative method to find
the smallest eigen value and corresponding eigen vector
of a matrix A. It is very similar to the power method, but
involves iterations that involve multiplication of the iterates
by A-1 (provided inverse exists) rather than A. We then
apply the standard power method to which will return the
largest eigenvalue of (say, λ’ ) and the corresponding
eigenvector (say,v’ ). The inverse of this eigenvalue, that
is, 1/λ’ will give the smallest eigenvalue of the matrix .
Please note that the eigenvector corresponding to λ in that
is, remains same as the eigenvector for 1/λ’ in A.
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6. Plot of iteration count and
falling errors
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Codes:
x=1:i-1
err=err(2:i)
plot(x,err)
7. Conclusion
• Hence we can verify the least
Eigen value by the built in function
• Trace gives the sum of eigenvalues to
calculate the remaining by subtracting
the dominant and least eigen value in
a 3*3 matrix
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