On high-order iterative schemes for the matrix pth root avoiding the use of inverses

This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first me...

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Detalles Bibliográficos
Autores: Amat Plata, Sergio, Busquier Sáez, Sonia, Hernández Verón, Miguel Ángel, Magreñán Ruiz, Ángel Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/10655
Acceso en línea:http://hdl.handle.net/10317/10655
https://www.mdpi.com/2227-7390/9/2/144
Access Level:acceso abierto
Palabra clave:Matrix pth root
Inverse operator
Iterative method
Order of convergence
Stability
Semilocal convergence
Matemática Aplicada
12 Matemáticas
Descripción
Sumario:This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.