chisl_meth / Лаб 6 QR-алгоритм, метод итераций / QR-A

Note that the true eigenvalues are 4.001 and 3.999.

Solution After computation we find

We see that as the theorem guarantees, is converging to an upper

triangular matrix and the diagonal elements are heading in the right direction; however, the convergence is very slow. The slowness of convergence is due to the fact that .

As we have seen, the convergence of the method can be slow: This

cosets money because of the computer time used. There exist methods for accelerating convergence of the method; these are covered in

advanced numerical analysis texts.

Finally, after we find the eigenvalues of , the corresponding eigenvectors can be found by solving , subject to some side condition such

as

Subsections

•PROBLEMS 6.3

•SUMMARY

•ADDITIONAL PROBLEMS

Next: PROBLEMS 6.3 Up: NUMERICAL CALCULATION OF EIGENVALUES

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