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1983•IEE Proceedings D Control Theory and ApplicationsRequires access

Some properties of matrix sign functions derived from continued fractions

L.S. Shieh, Y.T. Tsay, R.E. Yates

Open publisher page 37 citations

Abstract

This paper proposes an alternate representation of a matrix sign function based on an irrational function described by a continued fraction. The properties of the continued fraction and the truncated continued fractions are investigated. Also, new algorithms for computing the matrix sign function are developed. The matrix sign function is then extended to a generalised matrix sign function for directly solving discrete-time system problems.

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What this paper is about

This paper proposes an alternate representation of a matrix sign function based on an irrational function described by a continued fraction. The properties of the continued fraction and the truncated continued fractions are investigated. Also, new algorithms for computing the matrix sign function are developed. The matrix sign function is then extended to a generalised matrix sign function for directly solving discrete-time system problems.

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OpenAlex reports 37 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper proposes an alternate representation of a matrix sign function based on an irrational function described by a continued fraction. The properties of the continued fraction and the truncated continued fractions are investigated. Also, new algorithms for computing the matrix sign function are developed. The matrix sign function is then extended to a generalised matrix sign function for directly solving discrete-time system problems.

Key concepts: Sign (mathematics), Matrix (chemical analysis), Sign function, Mathematics, Matrix function, Function (biology), Fraction (chemistry), Applied mathematics

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