# A rational Arnoldi process with applications

@article{Pranic2016ARA, title={A rational Arnoldi process with applications}, author={Miroslav S. Pranic and Lothar Reichel and Giuseppe Rodriguez and Zhengsheng Wang and Xuebo Yu}, journal={Numerical Lin. Alg. with Applic.}, year={2016}, volume={23}, pages={1007-1022} }

Summary
The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non-Hermitian matrix A∈Cn×n and for the approximation of matrix functions. The method is particularly attractive when the rational functions that determine the process have only few distinct poles zj∈C, because then few factorizations of matrices of the form A − zjI have to be computed. We discuss recursion relations for orthogonal bases of rational Krylov subspaces determined by… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

## Enabling the international academic community to gain insight into the scientific activities of Banja Luka University mathematicians during the period 2007-2016

VIEW 10 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Computing unstructured and structured polynomial pseudospectrum approximations

VIEW 1 EXCERPT

CITES METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 28 REFERENCES

## Rational Krylov sequence methods for eigenvalue computation

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## and C

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Large-Scale Computation of Pseudospectra Using ARPACK and Eigs

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Calculation of Pseudospectra by the Arnoldi Iteration

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Functions of matrices - theory and computation

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Pseudospectra of rectangular matrices

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Rational Krylov subspace methods, in Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, eds

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Rational Krylov Algorithms for Nonsymmetric Eigenvalue Problems

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL