Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

J. S.H. Tsai; L. S. Shieh; R. E. Yates

doi:10.1016/0898-1221(88)90034-X

Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

J. S.H. Tsai, L. S. Shieh, R. E. Yates

Department of Electrical Engineering

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

11 Citations (Scopus)

Abstract

This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.

Original language	English
Pages (from-to)	903-913
Number of pages	11
Journal	Computers and Mathematics with Applications
Volume	15
Issue number	11
DOIs	https://doi.org/10.1016/0898-1221(88)90034-X
Publication status	Published - 1988

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/0898-1221(88)90034-X

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title = "Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function",

abstract = "This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.",

author = "Tsai, {J. S.H.} and Shieh, {L. S.} and Yates, {R. E.}",

note = "Funding Information: tThis work was supported in part by the U.S. Army Research Office, under contract DAAL-03-S7-K0001, and the U.S. Army Missile R&D Command, under Contract DAAH-01-85-CAI 11, and NASA-Johnson Space Center, under Contract NAG 9-21 I.",

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T1 - Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

AU - Tsai, J. S.H.

AU - Shieh, L. S.

AU - Yates, R. E.

N1 - Funding Information: tThis work was supported in part by the U.S. Army Research Office, under contract DAAL-03-S7-K0001, and the U.S. Army Missile R&D Command, under Contract DAAH-01-85-CAI 11, and NASA-Johnson Space Center, under Contract NAG 9-21 I.

PY - 1988

Y1 - 1988

N2 - This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.

AB - This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.

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IS - 11

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Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

Abstract

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