1. Look at the code for eigssymb and lanczosf and determine how to turn off reorthogonalization. Run your modified code with the symmetric matrix lshp2233 and test the results using residchk. Turn...

1.

Look at the code for eigssymb and lanczosf and determine how to turn off reorthogonalization. Run your modified code with the symmetric matrix lshp2233 and test the results using residchk. Turn reorthogonalization back on and execute the same steps. Explain the results.

2.

This problem investigates ghost eigenvalues.

The matrix ghosttest in the book software distribution is a
diagonal matrix with ghosttest(1,1) = 100 and ghosttest(100,100) = 10. The remaining diagonal elements are in the range ( The function lanczosfplot produces a plot of the Lanczos iteration number vs. the eigenvalues of T. Run it with m = 35 and reorthog = 0 and see if you can identify ghost eigenvalues. Run it again with reorthog = 1 and compare the results.

 Create the diagonal matrix defined in Example
 using
lambda_ lambda_ and
 Repeat part
 for this matrix using m = 50.