# Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix

Elsner L (1976)
Linear algebra and its applications 15(3): 235-242.

Journal Article | Published | English
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Noda established the superlinear convergence of an inverse iteration procedure for calculating the spectral radius and the associated positive eigenvector of a non-negative irreducible matrix. Here a new proof is given, based completely on the underlying order structure. The main tool is Hopf's inequality. It is shown that the convergence is quadratic.
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Elsner L. Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear algebra and its applications. 1976;15(3):235-242.
Elsner, L. (1976). Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear algebra and its applications, 15(3), 235-242.
Elsner, L. (1976). Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear algebra and its applications 15, 235-242.
Elsner, L., 1976. Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear algebra and its applications, 15(3), p 235-242.
L. Elsner, “Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix”, Linear algebra and its applications, vol. 15, 1976, pp. 235-242.
Elsner, L.: Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear algebra and its applications. 15, 235-242 (1976).
Elsner, Ludwig. “Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix”. Linear algebra and its applications 15.3 (1976): 235-242.
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