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On the convergence of matrix powers of a generalized linear operator in idempotent algebra. / Krivulin, N. K.; Romanovskii, I. V.

в: Journal of Mathematical Sciences, Том 142, № 1, 2007, стр. 1806-1816.

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Harvard

Krivulin, NK & Romanovskii, IV 2007, 'On the convergence of matrix powers of a generalized linear operator in idempotent algebra', Journal of Mathematical Sciences, Том. 142, № 1, стр. 1806-1816. https://doi.org/10.1007/s10958-007-0089-2

APA

Krivulin, N. K., & Romanovskii, I. V. (2007). On the convergence of matrix powers of a generalized linear operator in idempotent algebra. Journal of Mathematical Sciences, 142(1), 1806-1816. https://doi.org/10.1007/s10958-007-0089-2

Vancouver

Krivulin NK, Romanovskii IV. On the convergence of matrix powers of a generalized linear operator in idempotent algebra. Journal of Mathematical Sciences. 2007;142(1):1806-1816. https://doi.org/10.1007/s10958-007-0089-2

Author

Krivulin, N. K. ; Romanovskii, I. V. / On the convergence of matrix powers of a generalized linear operator in idempotent algebra. в: Journal of Mathematical Sciences. 2007 ; Том 142, № 1. стр. 1806-1816.

BibTeX

@article{06662c1fec5746b3a8ca757b0abbc40a,
title = "On the convergence of matrix powers of a generalized linear operator in idempotent algebra",
abstract = "The generalized linear operator on a vector space over a commutative semiring which has zero and identity elements, idempotent addition, and invertible multiplication is considered. Some useful inequalities for the norm, trace, and eigenvalue of matrix are established. Based on the inequalities, simple proofs are suggested for the convergence theorems for the growth rate of the norm and trace of powers of the operator to converge to its spectral radius as the exponent tends to infinity. It is shown that the general expression for the spectral radius can be obtained as a consequence of the theorems.",
author = "Krivulin, {N. K.} and Romanovskii, {I. V.}",
year = "2007",
doi = "10.1007/s10958-007-0089-2",
language = "English",
volume = "142",
pages = "1806--1816",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - On the convergence of matrix powers of a generalized linear operator in idempotent algebra

AU - Krivulin, N. K.

AU - Romanovskii, I. V.

PY - 2007

Y1 - 2007

N2 - The generalized linear operator on a vector space over a commutative semiring which has zero and identity elements, idempotent addition, and invertible multiplication is considered. Some useful inequalities for the norm, trace, and eigenvalue of matrix are established. Based on the inequalities, simple proofs are suggested for the convergence theorems for the growth rate of the norm and trace of powers of the operator to converge to its spectral radius as the exponent tends to infinity. It is shown that the general expression for the spectral radius can be obtained as a consequence of the theorems.

AB - The generalized linear operator on a vector space over a commutative semiring which has zero and identity elements, idempotent addition, and invertible multiplication is considered. Some useful inequalities for the norm, trace, and eigenvalue of matrix are established. Based on the inequalities, simple proofs are suggested for the convergence theorems for the growth rate of the norm and trace of powers of the operator to converge to its spectral radius as the exponent tends to infinity. It is shown that the general expression for the spectral radius can be obtained as a consequence of the theorems.

U2 - 10.1007/s10958-007-0089-2

DO - 10.1007/s10958-007-0089-2

M3 - Article

VL - 142

SP - 1806

EP - 1816

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 5013880