Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.8
Iterative and numerical eigenvalue methods
Real applications need eigenvalues of large matrices with decimal entries, where factoring a characteristic polynomial is hopeless. Iterative methods instead multiply, scale and repeat, closing in on eigenvalues to any accuracy the computer allows.
In this topic
- Why not use the polynomial?
- The idea behind the power method
- The power method, step by step
- Worked example: the power method
- How fast, and when it fails
- A sharper estimate for symmetric matrices
- The inverse power method
- Worked example: the inverse power method
- The QR algorithm and real software
- Common mistakes to avoid
- Key takeaways
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