Decompositions of a matrix by means of its dual matrices with applications

Ik-Pyo Kim; Arnold Kräuter

doi:10.1016/j.laa.2017.09.031

Decompositions of a matrix by means of its dual matrices with applications

Ik-Pyo Kim, Arnold Kräuter

Chair of Mathematics, Statistics and Geometry (380)

Daegu University, Gyeongbuk

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We introduce the Notion of dual matrices of an infinite Matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal Matrix. We present the Cholesky decomposition of the symmetric Pascal Matrix by means of ist dual Matrix. Decompositions of a Vandermonde Matrix are used to obtain variants of the Lagrange Interpolation polynomial of degree <=n that passes through the n+1 Points (i,q_i) for i=0,1,...,n.

Translated title of the contribution	Matrixzerlegungen mithilfe ihrer dualen Matrizen mit Anwendungen
Original language	English
Pages (from-to)	100-117
Number of pages	8
Journal	Linear algebra and its applications
Volume	537.2018
Issue number	15 January
Early online date	28 Sept 2017
DOIs	https://doi.org/10.1016/j.laa.2017.09.031
Publication status	Published - 2018

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10.1016/j.laa.2017.09.031

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title = "Decompositions of a matrix by means of its dual matrices with applications",

abstract = "We introduce the Notion of dual matrices of an infinite Matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal Matrix. We present the Cholesky decomposition of the symmetric Pascal Matrix by means of ist dual Matrix. Decompositions of a Vandermonde Matrix are used to obtain variants of the Lagrange Interpolation polynomial of degree <=n that passes through the n+1 Points (i,q_i) for i=0,1,...,n.",

author = "Ik-Pyo Kim and Arnold Kr{\"a}uter",

year = "2018",

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AU - Kim, Ik-Pyo

AU - Kräuter, Arnold

PY - 2018

Y1 - 2018

N2 - We introduce the Notion of dual matrices of an infinite Matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal Matrix. We present the Cholesky decomposition of the symmetric Pascal Matrix by means of ist dual Matrix. Decompositions of a Vandermonde Matrix are used to obtain variants of the Lagrange Interpolation polynomial of degree <=n that passes through the n+1 Points (i,q_i) for i=0,1,...,n.

AB - We introduce the Notion of dual matrices of an infinite Matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal Matrix. We present the Cholesky decomposition of the symmetric Pascal Matrix by means of ist dual Matrix. Decompositions of a Vandermonde Matrix are used to obtain variants of the Lagrange Interpolation polynomial of degree <=n that passes through the n+1 Points (i,q_i) for i=0,1,...,n.

U2 - 10.1016/j.laa.2017.09.031

DO - 10.1016/j.laa.2017.09.031

M3 - Article

SN - 0024-3795

VL - 537.2018

SP - 100

EP - 117

JO - Linear algebra and its applications

JF - Linear algebra and its applications

IS - 15 January

ER -

Decompositions of a matrix by means of its dual matrices with applications

Abstract

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Duale Matrizen, Matrizenfaktorisierungen und Lagrange-Interpolation

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Decompositions of a matrix by means of its dual matrices with applications

Abstract

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Duale Matrizen, Matrizenfaktorisierungen und Lagrange-Interpolation

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