## 30 Citations

Bounds for the relative change of singular values of a real matrix

- Mathematics
- 2007

This paper amis to derive bounds for the relative change in the singular values of a real matrix. Both the full column rank and the full row rank cases are considered. Two numerical experiments show…

Efficient numerical algorithms for constructing orthogonal generalized doubly stochastic matrices

- MathematicsApplied Numerical Mathematics
- 2019

Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices

- MathematicsInt. J. Comput. Math.
- 2011

The general bounds of multiplicative relative perturbation for diagonalizable matrices are presented, which are the improvement of recent results and are sharper than those in related literatures.

On perturbation bounds of generalized eigenvalues for diagonalizable pairs

- MathematicsNumerische Mathematik
- 2007

Two perturbation bounds of the diagonalizable pairs of generalized eigenvalues are given and these results extend the corresponding ones given by Sun in 1982.

Relative perturbation bounds for eigenpairs of diagonalizable matrices

- Computer Science, Mathematics
- 2018

Some uniform relative perturbation bounds for eigenvalues and eigenspaces of diagonalizable matrices under additive and multiplicative perturbations are presented.

New upper bounds for the spectral variation of a general matrix

- Mathematics
- 2017

Let A ∈ C n × n be a normal matrix with spectrum { λ i } i = 1 n , and let A ~ = A + E ∈ C n × n be a perturbed matrix with spectrum { λ ~ i } i = 1 n . If A ~ is still normal, the celebrated Hoffm...

THE EIGENVALUE PERTURBATION BOUND FOR

- Mathematics, Computer Science
- 2006

Some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices are presented, which improves some recent results.

Spectral variation bounds for diagonalisable matrices

- Mathematics
- 1997

SummaryThis note is related to an earlier paper by Bhatia, Davis, and Kittaneh [4]. For matrices similar to Hermitian, we prove an inequality complementary to the one proved in [4, Theorem 3]. We…

On interval estimates of perturbations of generalized eigenvalues for diagonalizable pairs

- Mathematics, Computer ScienceLinear Algebra and its Applications
- 2019

On symplectic eigenvalues of positive definite matrices

- Mathematics
- 2015

If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(A)) is a diagonal matrix with positive diagonal entries, which…

## References

SHOWING 1-10 OF 10 REFERENCES

A proof of a generalized van der Waerden conjecture on permanents

- Mathematics
- 1982

Let A be an n × n matrix. Denote by σ k (A) the sum of all subpermanents of A of order k. Then on the set of doubly stochastic matrices σ k attains its minimum only on the matrix .

The Complexity of Computing the Permanent

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1979

On perturbations of matrix pencils with real spectra

- Mathematics
- 1994

Perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil A -AB with real spectrum are developed. It is shown how the chordal distances between the generalized…

The Maximum Number of Disjoint Permutations Contained in a Matrix of Zeros and Ones

- MathematicsCanadian Journal of Mathematics
- 1964

A well-known consequence of the König theorem on maximum matchings and minimum covers in bipartite graphs (5) or of the P. Hall theorem on systems of distinct representatives for sets (4) asserts…

The even cycle problem for directed graphs

- Mathematics
- 1992

If each arc in a strongly connected directed graph of minimum in- degree and outdegree at least 3 is assigned a weight 0 or 1, then the resulting weighted directed graph has a directed cycle of even…

Additive decomposition of nonnegative matrices with applications to permanents and scalingt

- Mathematics
- 1988

Let U1 and U2 be compact subsets of m × n nonnegative matrices with prescribed row sums and column sums. Given A in U2 , we study the quantity and the matrices B in U1 that satisfy A−μ(U1;A)B is…