Article
Discrepancy Estimate of Normal Vectors
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Abstract
Let A be an s × s invertible matrix with integer entries and with eigenvalues |λi| > 1, i = 1, . . . , s. In this paper we prove explicitly that there exists a vector α, such that the discrepancy of the sequence {αAn}N is equal n=1 to O(N−1(log N)2s+3) for N −→ ∞. This estimate can be improved no more than on the logarithmic factor.
Keywords
Ergodic matrix, normal vector, discrepancy.
Citation
Levin, M. B. & Volinsky, I. L. (2008). Discrepancy estimate of normal vectors. Uniform Distribution Theory, 3(1), 19–33.
M. B. Levin and I. L. Volinsky, “Discrepancy estimate of normal vectors,” Uniform Distribution Theory, vol. 3, no. 1, pp. 19–33, 2008.
Levin MB, Volinsky IL. Discrepancy estimate of normal vectors. Uniform Distribution Theory. 2008;3(1):19–33.
Levin, M. B. and Volinsky, I. L. (2008), ‘Discrepancy estimate of normal vectors’, Uniform Distribution Theory, 3(1), pp. 19–33.
Levin, Mordechay B., and Irina L. Volinsky. “Discrepancy Estimate of Normal Vectors.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 19–33.
Levin, Mordechay B., and Irina L. Volinsky. “Discrepancy Estimate of Normal Vectors.” Uniform Distribution Theory 3, no. 1 (2008): 19–33.
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Published by: Engineering Journals
