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

Bunse, W.; Bunse-Gerstner, A.

doi:10.1090/S0025-5718-1982-0658217-4

Computation of bounds for the positive eigenvector of a nonnegative irreducible matrix by monotone iteration
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by W. Bunse and A. Bunse-Gerstner PDF

Math. Comp. 39 (1982), 125-131 Request permission

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.

References

Erich Bohl, Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen, Springer Tracts in Natural Philosophy, Vol. 25, Springer-Verlag, Berlin-New York, 1974 (German). MR 0636414
W. Robert Boland and C. S. Duris, Product type quadrature formulas, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 139–158. MR 292295, DOI 10.1007/bf01934362
Dietrich Braess, Die Konstruktion monotoner Iterationsfolgen zur Lösungseinschliessung bei linearen Gleichungssystemen, Arch. Rational Mech. Anal. 9 (1962), 97–106 (German). MR 137303, DOI 10.1007/BF00253336
J. W. Burgmeier and M. R. Scott, A method for obtaining bounds on eigenvalues and eigenfunctions by solving non-homogeneous integral equations, Computing (Arch. Elektron. Rechnen) 10 (1972), 9–22 (English, with German summary). MR 366063, DOI 10.1007/bf02242379
Günther Hämmerlin, Ein Ersatzkernverfahren zur numerischen Behandlung von Integralgleichungen 2. Art, Z. Angew. Math. Mech. 42 (1962), 439–463 (German, with English and Russian summaries). MR 187421, DOI 10.1002/zamm.19620421004
C. A. Hall and J. Spanier, Nested bounds for the spectral radius, SIAM J. Numer. Anal. 5 (1968), 113–125. MR 225477, DOI 10.1137/0705009
J. Sprekels and H. Voss, Ein Verfahren zur iterativen Einschliessung des positiven Eigenvektors einer irreduziblen, nichtnegativen Matrix, Computing 20 (1978), no. 1, 27–34 (German, with English summary). MR 478577, DOI 10.1007/BF02241899
Tetsuro Yamamoto, A computational method for the dominant root of a nonnegative irreducible matrix, Numer. Math. 8 (1966), 324–333. MR 218011, DOI 10.1007/BF02162977