Suchergebnisse - approximation by polynomials with integer coefficients

Uniform approximation by polynomials with integer coefficients von Lipnicki, Artur

“… ]\) with real coefficients, such that \(P^{(k)}(0)/k!\) and \(P^{(k)}(1)/k!\) are integers for \(k=0,\dots,r-1\). It is proved that there is a polynomial …”
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Geometric properties of the lattice of polynomials with integer coefficients von Lipnicki, Artur, mieta ski, Marek J.

“… This paper is related to the classic but still being examined issue of approximation of functions by polynomials with integer coefficients. Let \(r\), \(n …”
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Uniform Approximation by Polynomials with Integer Coefficients via the Bernstein Lattice von Güntürk, C Sinan, Li, Weilin

“… \(\mathbb{Z}[X]\) of polynomials with integer coefficients, when considered as a set of functions on \([0,1]\), is dense in \(\mathscr{C}_\mathbb{Z}([0,1 …”
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Best approximation of constants by polynomials with integer coefficients von Trigub, R., Volchkov, V.

“… What is best approximation of a non-integer number λ∈R by polynomials qn of degree at most n with integer coefficients on the segment [a,b]⊂(0,1 …”
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ON APPROXIMATION OF CONSTANTS BY POLYNOMIALS WITH INTEGER COEFFICIENTS von Trigub, R. M.

“… In this paper, the exact rate of decrease of best approximations of non-integer numbers by polynomials with integer coefficients is established …”
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Polynomial Function Approximations With Leading Integer Coefficients for Efficient Encrypted Implementations von Teichrib, Dieter, Adamek, Janis, Binfet, Philipp, Darup, Moritz Schulze

“… Specifically, we show that enforcing a leading integer coefficient enables the use of polynomials of one degree higher than all existing …”
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On the best approximation of non-integer constants by polynomials with integer coefficients von Trigub, Roald M.

“… The exact decrease rate of the best approximations of non-integer numbers by polynomials with integer coefficients of growing degrees is found on a disk in the complex plane, a cube in ℝ d , and a ball in ℝ d …”
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Approximation with One-Bit Polynomials in Bernstein Form von Güntürk, C. Sinan, Li, Weilin

“… We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order …”
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Polynomials with integer coefficients and Chebyshev polynomials von Trigub, Roal′d M.

“… The paper is devoted to the popularization of one of the topics at the border between analysis and number theory that is related to polynomial with integer …”
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Polynomials with integer coefficients and their zeros von Pritsker, Igor E.

“… We also discuss interesting applications to the approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets …”
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Simultaneous approximation by Bernstein polynomials with integer coefficients von Draganov, Borislav R

“… We prove that several forms of the Bernstein polynomials with integer coefficients possess the property of simultaneous approximation, that is, they approximate not only the function but also its derivatives …”
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Converse estimates for the simultaneous approximation by Bernstein polynomials with integer coefficients von Draganov, Borislav R

“… We prove a weak converse estimate for the simultaneous approximation by several forms of the Bernstein polynomials with integer coefficients …”
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On the best approximation of constants by polynomials with integer coefficients von Trigub, R M

“… In this paper, exact rate of decrease of best approximations of non-integer numbers by polynomials with integer coefficients of the growing exponentials …”
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Approximation of Smooth Functions and Constants by Polynomials with Integer and Natural Coefficients von Trigub, R. M.

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Polynomials with integer coefficients and their zeros von Pritsker, Igor E

“… We also discuss interesting applications to approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets …”
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Vertical Shift and Simultaneous Diophantine Approximation on Polynomial Curves von Adiceam, Faustin

“… is larger than the degree of P(X). This provides the first results related to the computation of the Hausdorff dimension of the set of well-approximable points lying on a curve that is not defined by a polynomial with integer coefficients …”
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Chebyshev Polynomials and Integer Coefficients von Trigub, R. M.

“… for nonzero polynomials with integer coefficients of arbitrary degree …”
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Minimizing Coefficients Wordlength for Piecewise-Polynomial Hardware Function Evaluation With Exact or Faithful Rounding von De Caro, Davide, Napoli, Ettore, Esposito, Darjn, Castellano, Gerardo, Petra, Nicola, Strollo, Antonio G. M.

“… The proposed technique, using Integer Linear Programming (ILP), optimizes the polynomial coefficients taking into account all error components simultaneously …”
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Approximation with one-bit polynomials in Bernstein form von Güntürk, C Sinan, Li, Weilin

“… We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order …”
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Searching worst cases of a one-variable function using lattice reduction von Stehle, D., Lefevre, V., Zimmermann, P.

“… Then, we show that this second problem can be solved efficiently by extending Coppersmith's work on the integer small value problem - for polynomials with integer coefficients - using lattice reduction …”
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