Timeline for Finding all roots of a polynomial
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2018 at 16:55 | comment | added | Denis Serre | @IgorBelegradek. True in general. But something remains. The obstacle to convergence is the fact that several eigenvalues have the same modulus. By choosing randomly a complex translation, all eigenvalues have distinct moduli, except for multiple eigenvalues. But then the QR method converges towards a block-triangular form, where each diagonal block has a single eigenvalue, which is the mean value of its diagonal elements. Therefore we still have a method to approximate efficiently the eigenvalues of a given matrix (up to a translation by $\alpha I_n$). | |
| Dec 15, 2018 at 16:28 | comment | added | Igor Belegradek | I talked to a local numerical algebra expert and according to him there is no no convergence theorem in the case of repeated eigenvalues. | |
| Aug 13, 2018 at 13:43 | comment | added | Igor Belegradek | Could you give a reference for the statement "the method does converge"? I spent some time looking through Watkins' "Fundamentals of matrix computations" which discusses the eigenvalue problem extensively, and was unable to find it. | |
| Aug 13, 2018 at 9:46 | history | answered | Denis Serre | CC BY-SA 4.0 |