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Results 1 - 10
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829
Boolean Circuit Complexity of Algebraic Interpolation Problems
- International Computer Science Institute, Berkeley
, 1989
"... . We present here some recent results on fast parallel interpolation of multivariate polynomials over finite fields. Some applications towards the general conversion algorithms for boolean functions are also formulated. Introduction We consider the general problem of interpolation of multivariate p ..."
Abstract
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Cited by 11 (8 self)
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. We present here some recent results on fast parallel interpolation of multivariate polynomials over finite fields. Some applications towards the general conversion algorithms for boolean functions are also formulated. Introduction We consider the general problem of interpolation of multivariate
Algebraic Multigrid Based On Element Interpolation (AMGe)
, 1998
"... We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the element stiffness matrices, AMGe is based on the use of two local measures, which are derived from global meas ..."
Abstract
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Cited by 104 (16 self)
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measures that appear in existing multigrid theory. These new measures are used to determine local representations of algebraically "smooth" error components that provide the basis for constructing effective interpolation and, hence, the coarsening process for AMG. Here, we focus
Interpolation in semigroupoid algebras
, 2005
"... A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class of semigroupo ..."
Abstract
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Cited by 11 (2 self)
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A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class
Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras
- OPERATOR THY
, 1998
"... The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to ..."
Abstract
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Cited by 73 (15 self)
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to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna–Pick type interpolation theorems.
INTERPOLATION SEQUENCES FOR THE BERNSTEIN ALGEBRA
, 808
"... ABSTRACT. We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line. Dedicated to Victor Petrovich Havin in his 75 birthday 1. ..."
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ABSTRACT. We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line. Dedicated to Victor Petrovich Havin in his 75 birthday 1.
Quasi-interpolation in the Fourier algebra
- J. Approx. Theory
, 2007
"... www.elsevier.com/locate/jat We derive new convergence results for the Schoenberg operator and more general quasi-interpolation operators. In particular, we prove that natural conditions on the generator function imply convergence of these operators in the Fourier algebra A(R d) = FL 1 (R d) and in ..."
Abstract
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Cited by 2 (2 self)
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www.elsevier.com/locate/jat We derive new convergence results for the Schoenberg operator and more general quasi-interpolation operators. In particular, we prove that natural conditions on the generator function imply convergence of these operators in the Fourier algebra A(R d) = FL 1 (R d
On the Lebesgue constant of subperiodic trigonometric interpolation
- J. Approx. Theory
"... We solve a recent conjecture, proving that the Lebesgue constant of Chebyshev-like angular nodes for trigonometric interpolation on a subinterval [−ω,ω] of the full period [−π,π] is attained at ±ω, its value is independent of ω and coincides with the Lebesgue constant of algebraic interpolation at t ..."
Abstract
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Cited by 5 (3 self)
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We solve a recent conjecture, proving that the Lebesgue constant of Chebyshev-like angular nodes for trigonometric interpolation on a subinterval [−ω,ω] of the full period [−π,π] is attained at ±ω, its value is independent of ω and coincides with the Lebesgue constant of algebraic interpolation
Algebraic Models of Computation and Interpolation for Algebraic Proof Systems
, 1998
"... this paper we are interested in systems that use uses polynomials instead of boolean formulas. From the previous list this includes the Nullstellensatz refutations. Recently a stronger system using polynomials was proposed, the polynomial calculus, also called the Groebner calculus [9]. The proof sy ..."
Abstract
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Cited by 23 (3 self)
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systems using lower bounds on circuit complexity. This method is based on proving computationally efficient versions of Craig's interpolation theorem for the proof system in question [14, 18]. For appropriate tautologies the interpolation theorem
Polynomial interpolation in several variables
, 2000
"... This is a survey of the main results on multivariate polynomial interpolation in the last twenty-five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique inter ..."
Abstract
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Cited by 71 (7 self)
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interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included.
Results 1 - 10
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829
