An inversion technique for certain patterned matrices

Kounias, Eustratios G.

doi:10.1016/0022-247x(68)90270-9

Cited by 7 publications

(2 citation statements)

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“…This matrix results from a statistical problem. [Kounias, 1968] The author Kounias provides explicit formulas for inverting some patterned matrices. For example, a tridiagonal Toeplitz matrix and a matrix completely filled with one element plus a diagonal are inverted.…”

Section: The Overviewmentioning

confidence: 99%

“…[ Uppuluri and Carpenter, 1970] Uppuluri and Carpenter calculate the inverse of a tridiagonal Toeplitz matrix (not necessarily symmetric) via the associated difference equation. The results are based on [Kounias, 1968]. [Capovani, 1970] Explicit formulas for the inverse of a nonsymmetric tridiagonal matrix are given by Capovani (no demands are placed on the elements of the tridiagonal).…”

Section: The Overviewmentioning

confidence: 99%

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A bibliography on semiseparable matrices*

Vandebril

Barel

Golub

et al. 2005

Calcolo

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Currently there is a growing interest in semiseparable matrices and generalized semiseparable matrices. To gain an appreciation of the historical evolution of this concept, we present in this paper an extensive list of publications related to the field of semiseparable matrices. It is interesting to see that semiseparable matrices were investigated in different fields, e.g., integral equations, statistics, vibrational analysis, independently of-each other. Also notable is the fact that leading statisticians at that time Used semiseparable matrices without knowing their inverses to be tridiagonal. During this historical evolution the definition of semiseparable matrices has always been a difficult point leading to misunderstandings; sometimes they were defined as the inverses of irreducible tridiagonal matrices leading to generator representable matrices, while in other cases they were defined as matrices having low rank blocks below the diagonal.

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Section: The Overviewmentioning

confidence: 99%

Section: The Overviewmentioning

confidence: 99%

A bibliography on semiseparable matrices*

Vandebril

Barel

Golub

et al. 2005

Calcolo

View full text Add to dashboard Cite

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Auflösung von Gleichungssystemen mit einer Bandmatrix

Berg

1977

Z Angew Math Mech

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Zur Auflösung großer Gleichungssysteme mit einer Bandmatrix wird ein Verfahren vorgeschlagen, mit dessen Hilfe das gegebene System auf einige kleine Systeme zurückgeführt wird. Dieses Verfahren enthält eine Reihe von Freiheitsgraden, deren Ausnutzung zu verschiedenen Varianten führt. Eine Variante liefert direkt die inverse Matrix. Bei den übrigen Varianten wird diskutiert, welcher Fall numerisch optimal ist. Weiterhin wird diskutiert, unter welchen Bedingungen numerische Stabilität zu erwarten ist. Bei tridiagonalen Matrizen ergeben sich geschlossene Formeln. Als Anwendungsbeispiel wird die näherungsweise Lösung eines Identifikationsproblems skizziert.

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