Non-commutative extrapolation algorithms

Salam, A.

doi:10.1007/bf02140685

Cited by 25 publications

(15 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Designants, introduced by Heyting in 1927 [29], are their counterpart for systems of linear equations in a non-commutative algebra and they are related to Schur complements. This notion is fundamental in the development of vector sequence transformations and it was extensively studied and used by Salam [37][38][39]. It could also be used for deriving the new transformations given in this section, as done in [15].…”

Section: The New Transformationsmentioning

confidence: 98%

New vector sequence transformations

Brezinski

Redivo–Zaglia

2004

Linear Algebra and its Applications

View full text Add to dashboard Cite

Many numerical methods produce sequences of vectors converging to the solution of a problem. When the convergence is slow, the sequence can be transformed into a new vector sequence which, under some assumptions, converges faster to the same limit. The construction of a sequence transformation is based on its kernel, that is the set of sequences which are transformed into a constant sequence. In this paper, new vector sequence transformations are built from kernels which extent those of the most general transformations known so far

show abstract

Section: The New Transformationsmentioning

confidence: 98%

New vector sequence transformations

Brezinski

Redivo–Zaglia

2004

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

“…We recall here only the definition for a system of two linear equations in two unknowns. For the general case and more details, see [15,25].…”

Section: Designantsmentioning

confidence: 99%

Vector Padé-Type Approximants and Vector Padé Approximants

Salam¹

1999

Journal of Approximation Theory

Self Cite

View full text Add to dashboard Cite

“…However, it was later proved by McLeod [23] that the kernel of this vector ε-algorithm is the set of vector sequences satisfying a relation of the same form as (1) with a i ∈ R. The proof was quite technical and it involved Clifford algebra. It was later showed that the vectors ε (n) 2k ∈ R m it computes are given by ratios of determinants of dimension 2k + 1 instead of k + 1 as in the scalar case [16], or by designants of dimension k + 1, objects that generalize determinants in a non-commutative algebra [27].…”

Section: The Topological Shanks Transformationsmentioning

confidence: 99%

The Simplified Topological $\varepsilon$-Algorithms for Accelerating Sequences in a Vector Space

Brezinski¹,

Redivo–Zaglia²

2014

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

When a sequence of numbers is slowly converging, it can be transformed into a new sequence which, under some assumptions, could converge faster to the same limit. One of the most well-known sequence transformation is Shanks transformation which can be recursively implemented by the ε-algorithm of Wynn. This transformation and this algorithm have been extended (in two different ways) to sequence of elements of a topological vector space E. In this paper, we present new algorithms of implementing these topological Shanks transformations. They no longer require the manipulation of elements of the algebraic dual space E * of E, nor using the duality product into the rules of the algorithms, they need the storage of less elements of E, and the stability is improved. They also allow us to prove convergence and acceleration results for some types of sequences. Various applications involving sequences of vectors or matrices show the interest of the new algorithms.

show abstract

Non-commutative extrapolation algorithms

Cited by 25 publications

References 19 publications

New vector sequence transformations

New vector sequence transformations

Vector Padé-Type Approximants and Vector Padé Approximants

The Simplified Topological $\varepsilon$-Algorithms for Accelerating Sequences in a Vector Space

Contact Info

Product

Resources

About