# Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis

@inproceedings{Dopico2018StrongLO, title={Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis}, author={Froil'an M. Dopico and Silvia Marcaida and Mar'ia C. Quintana}, year={2018} }

We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation. For this purpose, we combine the theory developed by Amparan et al., MIMS EPrint 2016.51, and the new linearizations of polynomial matrices introduced by Fa{\ss}bender and Saltenberger, Linear Algebra Appl., 525 (2017). In addition, we present a detailed study of how to recover eigenvectors of a rational matrix from… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 33 REFERENCES

## Strong Linearizations of Rational Matrices

VIEW 10 EXCERPTS

## On vector spaces of linearizations for matrix polynomials in orthogonal bases

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Vector Spaces of Linearizations for Matrix Polynomials

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Block Kronecker linearizations of matrix polynomials and their backward errors

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## State-space and multivariable theory,

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL