# Avoiding look-ahead in the Lanczos method and Padé approximation

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 1, page 33-62
- ISSN: 1233-7234

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topAyachour, E.. "Avoiding look-ahead in the Lanczos method and Padé approximation." Applicationes Mathematicae 26.1 (1999): 33-62. <http://eudml.org/doc/219225>.

@article{Ayachour1999,

abstract = {In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for solving systems of linear equations is discussed.},

author = {Ayachour, E.},

journal = {Applicationes Mathematicae},

keywords = {extrapolation methods; orthogonal and biorthogonal polynomials; Padé approximation; Lanczos method; regular orthogonal polynomials; singular orthogonal polynomials; triangular linear systems; avoiding look-ahead},

language = {eng},

number = {1},

pages = {33-62},

title = {Avoiding look-ahead in the Lanczos method and Padé approximation},

url = {http://eudml.org/doc/219225},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Ayachour, E.

TI - Avoiding look-ahead in the Lanczos method and Padé approximation

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 1

SP - 33

EP - 62

AB - In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for solving systems of linear equations is discussed.

LA - eng

KW - extrapolation methods; orthogonal and biorthogonal polynomials; Padé approximation; Lanczos method; regular orthogonal polynomials; singular orthogonal polynomials; triangular linear systems; avoiding look-ahead

UR - http://eudml.org/doc/219225

ER -

## References

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