Re: high-precision eigenvalue solver

In case he needs the small difference of two non-small eigenvalues he
can separate them with shifted inverse iteration, the shift being
approximately the average of the two eigenvalues.
Hans Mittelmann

.

Relevant Pages

  • Re: convergence of QR-algorithm
    ... Bill, yes I'm doing all of that., alongside using a shift that is the ... calculate the eigenvalues of this. ... In either case the bottom two elements below the diagonal should ... the one I'm using as it involves more calculation at each iteration. ...
    (sci.math.num-analysis)
  • Re: Why the error in this 2x2 eigenvalue computation?
    ... (Peter Spellucci) ... double shift is a shift and its conjugate, but I thought it would be ... I don't believe that eig() will do shifts on a 2 by 2 problem, ... those shifts are taken anyway as the eigenvalues of the right lower ...
    (sci.math.num-analysis)
  • Re: QR algorithm with explicit shifts
    ... and then carries out iterations of the QR algorithm until one ... >of the eigenvalues converges. ... >another shift and carries on with the QR algorithm until the next eigenvalue ... with regards to how quickly overall convergence is ...
    (sci.math.num-analysis)
  • Re: incorrect convergence of qr algorithm
    ... >> i have written an eigenvalue finder that uses the qr algorithm, ... i seem to get the wrong values upon convergence. ... have all eigenvalues on the unit circle in the complex plane. ... then complex eigenvalues appear as complex conjugates and no real shift can break ...
    (sci.math.num-analysis)
  • QR algorithm with explicit shifts
    ... a real or complex matrix. ... the way i have it set up at present is that it selects a shift (a wilkinson ... shift taken from the eigenvalues of the bottom right hand corner 2 x 2 ... and then carries out iterations of the QR algorithm until one ...
    (sci.math.num-analysis)