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## Sparse Polynomial Square -- from Wolfram MathWorld

Sparse Polynomial Square. A sparse polynomial square is a square of a polynomial that has fewer terms than the original polynomial .Examples include Rényi's polynomial

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## Sparse Polynomials and Matrices

To lay groundwork for programming project Materials: 1. Handout of Polynomial class - .h, .cc, tester I. Sparse Polynomials - ----- ----- A. As an illustration of a situation in which alternative data structures might be used, we consider the problem of representing a polynomial. 1.

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## Sparse - definition of sparse by The Free Dictionary

Define sparse. sparse synonyms, sparse pronunciation, sparse translation, English dictionary definition of sparse. adj. spars·er , spars·est Occurring, growing, or settled at widely spaced intervals; not thick or dense. sparse′ly adv. sparse′ness , spar′si·ty n.

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## Solving sparse polynomial optimization problems with ...

1/5/2018 · The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value.

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## Sparse Matrix and Polynomial - SlideShare

2/3/2015 · This is about Data Structure- sparse matrix and polynomial. in a matrix, have many of its elements is zero is known as sparse matrix. This is about Data Structure- sparse matrix and polynomial. in a matrix, have many of its elements is zero is known as sparse matrix.

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## Adaptive sparse polynomial dimensional decomposition for ...

A significance is that uncertain parameters are not restricted to be random variables in the Polynomial Chaos Askey scheme. The novelty of this approach is that with it we can compute all DSI using a sparse surrogate built from a polynomial dimensional decomposition, which is a series in multivariate orthonormal polynomials.

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## Arageli::sparse_polynom< F, I, REFCNT > Class Template ...

If ‘refcounting’ is false this is empty operation. Otherwise if reference counter value is one (only this descriptor refers to) then immediate returns true. Else create for this descriptor new clean internal representation object (zeroth polynomial) and return false. Definition at line 1187 of file sparse_polynom.hpp.

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## Sparse polynomial interpolation: compressed sensing, super ...

P A sparse polynomial is a polynomial z 7→ g(z) = α gα zα with only a few non-zero coefficients (gα ) and sparse interpolation is concerned with recovering the unknown monomials (zα ) and coefficients (gα ) of a sparse polynomial via the sole knowledge of a few (and as few as possible) values of g at some points (zk ) ⊂ Cn that one ...

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## A POLYHEDRAL METHOD FOR SOLVING SPARSE POLYNOMIAL …

A POLYHEDRAL METHOD FOR SOLVING SPARSE POLYNOMIAL SYSTEMS BIRKETT HUBER AND BERND STURMFELS Abstract. A continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations. We introduce mixed subdivisions of Newton polytopes, and we apply them to give a new proof and

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## (PDF) Solving sparse polynomial optimization problems with ...

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under

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## Sparse Polynomial Interpolation With Arbitrary Orthogonal ...

Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp--Massey algorithm. ...

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## (PDF) Noisy interpolation of sparse polynomials in finite ...

PDF | We consider a polynomial analogue of the hidden number problem introduced by Boneh and Venkatesan, namely the sparse polynomial noisy interpolation problem of recovering an unknown ...

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## (PDF) Sparse Polynomial Division Using a Heap | Roman ...

Sparse Polynomial Division Using a Heap Michael Monagan Department of Mathematics, Simon Fraser University Burnaby B.C. V5A 1S6, Canada Roman Pearce Department of Mathematics, Simon Fraser University Burnaby B.C. V5A 1S6, Canada Abstract In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap.

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## Dense graph - Wikipedia

In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges, is a sparse graph.The distinction between sparse and dense graphs is rather vague, and depends on the context.

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## Sparse legal definition of sparse - TheFreeDictionary.com

A female member of a hook-and-loop fastener formed of a fibrous material, the female member engageable with a mating male member, the female member comprising: a plurality of lines of dense fiber portions in which the fibrous material has a high basis weight; and a plurality of lines of sparse fiber portions provided between the dense fiber ...

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