Fetching the paper…

Reading the bibliography…

2011

La Budde's Method for Computing Characteristic Polynomials

Rehman, Rizwana, Ipsen, Ilse C. F.

Original
PDF
Post on X

Understand

La Budde's method computes the characteristic polynomial of a real matrix A in two stages: first it applies orthogonal similarity transformations to reduce A to upper Hessenberg form H, and second it computes the characteristic polynomial of H from characteristic polynomials of leading principal submatrices of H.

If A is symmetric, then H is symmetric tridiagonal, and La Budde's method simplifies to the Sturm sequence method.
If A is diagonal then La Budde's method reduces to the Summation Algorithm, a Horner-like scheme used by the MATLAB function POLY to compute characteristic polynomials from eigenvalues.
We present recursions to compute the individual coefficients of the characteristic polynomial in the second stage of La Budde's method, and derive running error bounds for symmetric and nonsymmetric matrices.

La Budde's Method for Computing Characteristic Polynomials · Around

Built on

P. Horst
1935
Earlier work this paper cites.
M. D. Bingham
1941
Earlier work this paper cites.
P. A. Samuelson
1942
Earlier work this paper cites.
W. B. Givens
1953
Earlier work this paper cites.
V. N. Faddeeva
1959
Earlier work this paper cites.
A. S. Householder and F. L. Bauer
1959
Earlier work this paper cites.
E. R. Hansen
1963
Earlier work this paper cites.
A. S. Householder
1964
Earlier work this paper cites.
J. Wilkinson
1965
Earlier work this paper cites.
S. J. Hammarling
1970
Earlier work this paper cites.

Similar

C. Papaconstantinou
1974
Cited alongside, same era.
L. Csanky
1976
Cited alongside, same era.
J. Wang and C.-T. Chen
1982
Cited alongside, same era.
J. H. Wilkinson
1984
Cited alongside, same era.
D. H. Wiedemann
1986
Cited alongside, same era.
S. Barnett
1989
Cited alongside, same era.
E. Kaltofen and B. D. Saunders
1991
Cited alongside, same era.
G. Helmberg, P. Wagner, and G. Veltkamp
1993
Cited alongside, same era.

Then

M. Giesbrecht
1995
Later among the works it cites.
P. Misra, E. Quintana, and P. Van Dooren
1995
Later among the works it cites.
G. H. Golub and C. F. Van Loan
1996
Later among the works it cites.
F. R. Gantmacher
1998
Later among the works it cites.
S.-H. Hou
1998
Later among the works it cites.
N. J. Higham
2002
Later among the works it cites.
D. Lee and T. Schaefer
2005
Later among the works it cites.
I. Ipsen and R. Rehman
2008

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

M. Lewin

1994

Cited alongside, same era.

In revision

R. Rehman and I. Ipsen

Cited in the paper.

Later among the works it cites.

R. Rehman

2010

Later among the works it cites.