Search Results - approximation by polynomials with integer coefficients

Uniform approximation by polynomials with integer coefficients by 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…”
Get full text

Geometric properties of the lattice of polynomials with integer coefficients by 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…”
Get full text

Uniform Approximation by Polynomials with Integer Coefficients via the Bernstein Lattice by 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…”
Get full text

Best approximation of constants by polynomials with integer coefficients by 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…”
Get full text

ON APPROXIMATION OF CONSTANTS BY POLYNOMIALS WITH INTEGER COEFFICIENTS by 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…”
Get full text

Polynomial Function Approximations With Leading Integer Coefficients for Efficient Encrypted Implementations by 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…”
Get full text

On the best approximation of non-integer constants by polynomials with integer coefficients by 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…”
Get full text

Approximation with One-Bit Polynomials in Bernstein Form by Güntürk, C. Sinan, Li, Weilin

“…We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order…”
Get full text

Polynomials with integer coefficients and Chebyshev polynomials by 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…”
Get full text

Polynomials with integer coefficients and their zeros by 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…”
Get full text

Simultaneous approximation by Bernstein polynomials with integer coefficients by 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…”
Get full text

Converse estimates for the simultaneous approximation by Bernstein polynomials with integer coefficients by Draganov, Borislav R

“…We prove a weak converse estimate for the simultaneous approximation by several forms of the Bernstein polynomials with integer coefficients…”
Get full text

On the best approximation of constants by polynomials with integer coefficients by 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…”
Get full text

Approximation of Smooth Functions and Constants by Polynomials with Integer and Natural Coefficients by Trigub, R. M.

Get full text

Polynomials with integer coefficients and their zeros by 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…”
Get full text

Vertical Shift and Simultaneous Diophantine Approximation on Polynomial Curves by 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…”
Get full text

Chebyshev Polynomials and Integer Coefficients by Trigub, R. M.

“… for nonzero polynomials with integer coefficients of arbitrary degree…”
Get full text

Minimizing Coefficients Wordlength for Piecewise-Polynomial Hardware Function Evaluation With Exact or Faithful Rounding by 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…”
Get full text

Approximation with one-bit polynomials in Bernstein form by Güntürk, C Sinan, Li, Weilin

“…We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order…”
Get full text

Searching worst cases of a one-variable function using lattice reduction by 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…”
Get full text