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We present an alternative pathway in the application of the variationimprovement of ordinary perturbation theory exposed in [1] which can preservethe internal symmetries of a model by means of a time compactification.Comment: 21 pages, 4 Postscript figures available through anonymous ftp at  ftp://algol.lpm.univ-montp2.fr ; replaces version which could not be  postscripted presumably for lack of figures.uu fil

CONVERGENT SEQUENCES OF PERTURBATIVE APPROXIMATIONS FOR THE ANHARMONIC OSCILLATOR II: COMPACT TIME APPROACH