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ApproximateSecret Sharing in Field of Real Numbers. [PDF]
Entropy (Basel)Wan J, Wang Z, Yu Y, Yan X.
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Lightweight XOR-based visual cryptography using random shares for secure colour image sharing with minimal shares. [PDF]
Sci RepNujumudeen F, Mubarak DMN, Hussain T.
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On the Complexity of Polynomial Zeros
SIAM Journal on Computing, 1992An algorithm for simultaneous approximation of all zeros of a polynomial introduced by Householder is considered. A modification suitable for parallel computation is proposed. The root-finding problem for a polynomial of degree \(n\), having zeros \(z_ i\), \(i=1,\dots,n\) is \(NC\)- reduced to finding a polynomial \(\alpha(z)\) such that \(| \alpha(z_{
BINI, DARIO ANDREA, GEMIGNANI, LUCA
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Polynomials and Complex Polynomials
1997If F is a field and n is a nonnegative integer, then a polynomial of degree n over F is a formal sum of the form $$P(x) = {a_0} + {a_1}x + \cdots + {a_n}{x^n}$$ With a i ∈ F for i = 0, .., n, a n ≠ 0 and x an indeterminate. A polynomial P(χ) over F is either a polynomial of some degree or the expression P(χ) = 0, which is called the zero ...
Benjamin Fine, Gerhard Rosenberger
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Complex polynomial phase integration
IEEE Transactions on Antennas and Propagation, 1985A previously published integration algorithm applicable to the numerical computation of integrals with rapidly oscillating integrands is generalized. The previous algorithm involved quadratic approximation of the phase function which was assumed to be real. The present generalization concerns approximation of a complex phase function by a polynomial of
R. Pogortzelski, D. Mallery
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2002
This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
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This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
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Generating complex orthogonal polynomials
Integral Transforms and Special Functions, 2008Abstract The half-function concept is queried. It is argued that this concept is neither strict nor necessary. Without involving the half-function, the procedure of heuristically constructing complex orthogonal polynomials is presented.
Kui Fu Chen, Jian Li Wang
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1993
We consider the complex polynomial p: C → C defined by $$p(z)=\sum\limits_{i=0}^n{{p_i}{z^i}},{p_i}\in\mathbb{C}{\text{, }}i=0, . . . , n, {p_n}\ne 0.$$ (1) (9.1) The Fundamental Theorem of algebra asserts that this polynomial has n zeros counted by multiplicity. Finding these roots is a non trivial problem in numerical mathematics.
Ulrich Kulisch +3 more
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We consider the complex polynomial p: C → C defined by $$p(z)=\sum\limits_{i=0}^n{{p_i}{z^i}},{p_i}\in\mathbb{C}{\text{, }}i=0, . . . , n, {p_n}\ne 0.$$ (1) (9.1) The Fundamental Theorem of algebra asserts that this polynomial has n zeros counted by multiplicity. Finding these roots is a non trivial problem in numerical mathematics.
Ulrich Kulisch +3 more
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