Borinage
Borinage , region, Hainaut prov., S Belgium, surrounding Mons and extending to the French border. Traditionally a coal-mining district, most of the mines have been closed. Glass-making and metallurgy are the region's primary industries.
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Orthogonal polynomials and recurrence equations, operator equations and factorization.
Magazine article from: Electronic Transactions on Numerical Analysis; 4/1/2007; ; 700+ words
; ...orthogonal polynomials can be defined as the common polynomial solutions...all these polynomial systems are...the Bessel polynomials is not defined...orthogonal polynomials can be defined as the polynomial solutions of...
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Solving polynomials with computers.
Magazine article from: American Scientist; 1/1/1998; ; 700+ words
; ...about the roots of polynomials. The problem of finding exact solutions to polynomials was definitively...can be no universal polynomial-solving formula in...approaches to solving polynomials, the crucial factor...called the degree of the polynomial. The ancient Egyptians...
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Gegenbauer polynomials and semiseparable matrices.(Report)
Magazine article from: Electronic Transactions on Numerical Analysis; 1/1/2008; ; 700+ words
; ...1]. Gegenbauer polynomials [C.sup.([alpha...complete set of orthogonal polynomial solutions to the more...classical orthogonal polynomials mention Gegenbauer...families of Gegenbauer polynomials in [24] but the connection...evaluation of orthogonal polynomial expansions at Chebyshev...
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Polynomial best constrained degree reduction in strain energy.
Magazine article from: Electronic Transactions on Numerical Analysis; 1/1/2007; ; 700+ words
; ...respect to Jacobi orthogonal polynomials. Then we give explicitly...Key words. reduction, polynomials, approximation, Bezier...Degree reduction of polynomials consists in approximating a given polynomial f (t) by a lower degree...
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Asymptotics of polynomial solutions of a class of generalized lame differential equations.
Magazine article from: Electronic Transactions on Numerical Analysis; 1/1/2005; ; 700+ words
; ...Heine-Stieltjes polynomial. In the simplest...Heine-Stieltjes polynomials are just hypergeometric...possible Van Vleck polynomials C for which (1...Heine-Stieltjes polynomial y = [psi] of...are Van Vleck polynomials. In other words...there exists a polynomial solution y...
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Jacobi-weighted orthogonal polynomials on triangular domains.
Magazine article from: Journal of Applied Mathematics; 1/1/2005; ; 700+ words
; ...Bernstein polynomial basis. 1...orthogonal polynomials, a subject...defined. These polynomials [P.sub...orthogonal to each polynomial of degree...Bernstein polynomial basis. We show that these polynomials [P.sup...
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Duality of q-polynomials, orthogonal on countable sets of points.
Magazine article from: Electronic Transactions on Numerical Analysis; 8/1/2006; ; 700+ words
; ...Key words. q-orthogonal polynomials, duality, Jacobi matrix...2, ... , of orthogonal polynomials in one variable corresponds...indeterminate moment problem. If a polynomial family corresponds to the...measure [mu] for these polynomials and they constitute a complete...
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Alternative orthogona; polynomials and quadratures.
Magazine article from: Electronic Transactions on Numerical Analysis; 12/1/2006; ; 700+ words
; ...to construct sequences of polynomials, which are orthogonal over...Key words. orthogonal polynomial, recurrence relation, quadrature...the classical orthogonal polynomials originates from a problem...requirements [8]. The polynomials also may be defined by an...
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Numerical condition of polynomials in different forms.
Magazine article from: Electronic Transactions on Numerical Analysis; 1/1/2001; ; 700+ words
; ...investigated the effect of polynomial bases on the condition...condition numbers of polynomials in the power, orthogonal...2. Condition of polynomial evaluation and polynomial zero. Let [P...denote the set of polynomials with complex coefficients...
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On rational classical orthogonal polynomials and their application for explicit computation of inverse laplace transforms.
Magazine article from: Mathematical Problems in Engineering; 1/1/2005; ; 700+ words
; ...classical orthogonal polynomials, we give three...classical orthogonal polynomials are special cases of the polynomial solutions of the...to classify the polynomial solutions of...i) Jacobi polynomials [{[P.sup...
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Polynomials
Encyclopedia entry from: The Gale Encyclopedia of Science
...conjunction with polynomials. The degree of a polynomial is the exponent...irreducible polynomials, just as every...numbers. A polynomial in two variables...definitions apply to polynomials in 3, 4...x201C; polynomial ”...
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polynomial
Book article from: A Dictionary of Computing
...If a r = 1, the polynomial is monic . Arithmetic on polynomials consists primarily...remainder. Every such polynomial can be uniquely...factors. The set of polynomials (over a field...monic irreducible polynomial (over the same...
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polynomial space
Book article from: A Dictionary of Computing
polynomial space A way of characterizing the complexity of an algorithm...polynomially bounded, the algorithm is said to be executable in polynomial space. Many problems for which no polynomial time algorithms have been found, nevertheless can easily...
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polynomial time
Book article from: A Dictionary of Computing
polynomial time A way of characterizing the complexity...increases with n no more rapidly than a polynomial p ( n ), f ( n ) ← p ( n...program is said to be executable in polynomial time. Here time is identified with...
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cycle index polynomial
Book article from: A Dictionary of Computing
cycle index polynomial A formal polynomial associated with a group of permutations on a set, indicating the decomposition of the permutations into cycles . Such polynomials occur for example in switching theory .
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