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Computation of bounds for the positive eigenvector of a nonnegative irreducible matrix by monotone iteration

Authors: W. Bunse and A. Bunse-Gerstner
Journal: Math. Comp. 39 (1982), 125-131
MSC: Primary 65F15; Secondary 15A42
MathSciNet review: 658217
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Abstract: A method for the computation of iterative bounds for the positive eigenvector of a nonnegative irreducible matrix is presented. It is based on the P-boundedness of the corresponding fixed point operator. Admissible initial bounds can be obtained by conditional preiteration.

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  • [1] E. Bohl, Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen, Springer-Verlag, Berlin, Heidelberg and New York, 1974. MR 0636414 (58:30525)
  • [2] W. R. Boland & C. S. Duris, "Product type quadrature rules," BIT, v. 11, 1971, pp. 139-158. MR 0292295 (45:1382)
  • [3] D. Braess, "Die Konstruktion monotoner Iterationsfolgen zur Lösungseinschließung bei linearen Gleichungssystemen," Arch. Rational Mech. Anal., v. 9, 1962, pp. 97-106. MR 0137303 (25:755)
  • [4] J. W. Burgmeier & M. R. Scott, "A method for obtaining bounds on eigenvalues and eigenfunctions by solving non-homogeneous integral equations," Computing, v. 10, 1972, pp. 9-22. MR 0366063 (51:2314)
  • [5] G. Hämmerlin, "Ein Ersatzkernverfahren zur numerischen Behandlung von Integralgleichungen 2. Art," Z. Angew. Math. Mech., v. 42, 1962, pp. 439-463. MR 0187421 (32:4873)
  • [6] C. A. Hall & J. Spanier, "Nested bounds for the spectral radius," SIAM J. Numer. Anal., v. 5, 1968, pp. 113-125. MR 0225477 (37:1070)
  • [7] J. Sprekels & H. Voss, "Ein Verfahren zur iterativen Einschließung des positiven Eigenvektors einer irreduziblen, nichtnegativen Matrix," Computing, v. 20, 1978, pp. 27-34. MR 0478577 (57:18054)
  • [8] T. Yamamoto, "A computational method for the dominant root of a non-negative irreducible matrix," Numer. Math., v. 8, 1966, pp. 324-333. MR 0218011 (36:1100)

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Article copyright: © Copyright 1982 American Mathematical Society

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