On an iterative algorithm converging to the solution of XCX=D

Based on a modified Newton method in the Banach algebra of square matrices, we construct here a simple iterative algorithm that converges to the unique positive solution of the algebraic Riccati equation X C X = D . Numerical examples illustrating the theoretical study and showing the speed of conve...

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Vydáno v:Afrika mathematica Ročník 31; číslo 5-6; s. 997 - 1007
Hlavní autoři: Al-Harbi, Nawal, Raïssouli, Mustapha
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020
Springer Nature B.V
Témata:
Applications of Mathematics
Banach spaces
Convergence
History of Mathematical Sciences
Iterative algorithms
Iterative methods
Mathematics
Mathematics and Statistics
Mathematics Education
Newton methods
Riccati equation
Modified algorithm
Directional derivative
Positive invertible matrix
Algebraic Riccati equation
26A51
15A24
47A64
Newton algorithm for matrix equations
15A60
ISSN:1012-9405, 2190-7668
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Shrnutí:Based on a modified Newton method in the Banach algebra of square matrices, we construct here a simple iterative algorithm that converges to the unique positive solution of the algebraic Riccati equation X C X = D . Numerical examples illustrating the theoretical study and showing the speed of convergence of our approach are discussed as well. At the end, we put some open questions as purposes for future research.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-020-00776-3