Article
Discrepancy Estimate of Normal Vectors (The Case of Hyperbolic Matrices)
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Abstract
Let A be a t × t invertible matrix with integer entries and with eigenvalues |λi| =6 1, i ∈ [1, t]. In this paper we prove explicitly that there ex- ists a vector α, such that discrepancy of the sequence {αAn}N n=1 is equal to O(N−1(log N)t+5) for N −→ ∞. This estimate can be improved no more than on the logarithmic factor.
Keywords
Hyperbolic matrix, normal vector, uniform distribution, discrepancy.
Citation
Levin, M. B. & Volinsky, I. L. (2010). Discrepancy estimate of normal vectors (the case of hyperbolic matrices). Uniform Distribution Theory, 5(2), 141–167.
M. B. Levin and I. L. Volinsky, “Discrepancy estimate of normal vectors (the case of hyperbolic matrices),” Uniform Distribution Theory, vol. 5, no. 2, pp. 141–167, 2010.
Levin MB, Volinsky IL. Discrepancy estimate of normal vectors (the case of hyperbolic matrices). Uniform Distribution Theory. 2010;5(2):141–167.
Levin, M. B. and Volinsky, I. L. (2010), ‘Discrepancy estimate of normal vectors (the case of hyperbolic matrices)’, Uniform Distribution Theory, 5(2), pp. 141–167.
Levin, Mordechay B., and Irina L. Volinsky. “Discrepancy Estimate of Normal Vectors (the Case of Hyperbolic Matrices).” Uniform Distribution Theory, vol. 5, no. 2, 2010, pp. 141–167.
Levin, Mordechay B., and Irina L. Volinsky. “Discrepancy Estimate of Normal Vectors (the Case of Hyperbolic Matrices).” Uniform Distribution Theory 5, no. 2 (2010): 141–167.
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Published by: Engineering Journals
