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In this paper we study the approximate minimization problem for language modelling.
The approximation of one matrix by another of lower rank
C. Eckart and G. Young · 1936
Earlier work this paper cites.
Functional Analysis [by] Frigyes Riesz and Béla Sz.-Nagy. Translated from the 2nd French ed. by Leo F. Boron
Frigyes Riesz and Béla Szökefalvi-Nagy · 1955
Earlier work this paper cites.
On Bounded Bilinear Forms
Zeev Nehari · 1957
Earlier work this paper cites.
Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space , volume 18 of Translations of Mathematical Monographs
M. Kreĭn and I. Gohberg · 1969
Earlier work this paper cites.
Analytic Properties of Schmidt Pairs for a Hankel Operator and the Generalized Schur–Takagi problem
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Earlier work this paper cites.
Realizations by stochastic finite automata
J.W. Carlyle and A. Paz · 1971
Earlier work this paper cites.
Matrice de Hankel
Michel Fliess · 1974
Earlier work this paper cites.
Fast Algorithms for Partial Fraction Decomposition
H. T. Kung and D. M. Tong · 1977
Earlier work this paper cites.
Optimal Hankel-Nnorm Model Reductions: Scalar Systems
Sun-Yuan Kung · 1980
Earlier work this paper cites.
Optimal Hankel-Norm Model Reductions: Multivariable Systems
Sun-Yuan Kung and David W. Lin · 1981
Earlier work this paper cites.
All Optimal Hankel–Nnorm Approximations of Linear Multivariable Systems and their ℒ ∞ \mathcal{L}^{\infty} –Error Bounds
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Earlier work this paper cites.
Optimal Hankel norm model reductions and Wiener–Hopf factorization I: The canonical case
Joseph A. Ball and Andre CM. Ran · 1987
Earlier work this paper cites.
Realisation and Approximation of Linear Infinite–Dimensional Systems with Error Bounds
Keith Glover, Ruth F Curtain, and Jonathan R Partington · 1988
Earlier work this paper cites.
System Reduction Via Truncated Hankel Matrices
Charles K Chui, Xin Li, and Joseph D Ward · 1991
Earlier work this paper cites.
Rate of Convergence of Schmidt Pairs and Rational Functions Corresponding to Best Approximants of Truncated Hankel Operators
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Earlier work this paper cites.
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Earlier work this paper cites.
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M.M Al-Hussari, I.M. Jaimoukha, and D.J.N. Limebeer · 1993
Earlier work this paper cites.
Über das Verhalten von Eigenwerten bei adiabatischen Prozessen , pages 294–297
J. von Neumann and E. P. Wigner · 1993
Earlier work this paper cites.
Continuity of Best Hankel Approximation and Convergence of Near–Best Approximants
Charles K. Chui and Xin Li · 1994
Earlier work this paper cites.
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Earlier work this paper cites.
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Cited alongside, same era.
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