The computational complexity of general change of basis algorithms from one bivariate polynomial basis of degree n to another bivariate polynomial basis of degree n using matrix multiplication is O(n 4). Applying blossoming and duality, we derive change of basis algorithms with computational complexity O(n 3) between two important classes of polynomial bases used for representing surfaces in CA...

In this paper, a closed-loop location-inventory problem for spare parts is presented. The proposed supply chain network includes two echelons, namely (1) distribution centers (DCs) and repairing centers (RCs) and (2) operational bases. Multiple spare parts are distributed among operational bases from distribution centers in the forward supply chain and failed spare parts from operational bases ...

In this paper, we extend the idea of comprehensive Gröbner bases given by Weispfenning (1992) to border bases for zero dimensional parametric polynomial ideals. For this, we introduce a notion of comprehensive border bases and border system, and prove their existence even in the cases where they do not correspond to any term order. We further present algorithms to compute comprehensive border b...

Efficient multiplication in finite fields Fqn requires Fq-bases of low density,i.e., such that the products of the basis elements have a sparse expression in the basis. In this paper we introduce a new family of bases: the quasi-normal bases. These bases generalize the notion of normal bases and provide simple exponentiation to the power q in Fqn . For some extension fields Fqn over Fq, we cons...

The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and two bases are connected by an edge if and only if one can be obtained from the other by the exchange of a single pair of elements. In this paper we prove that a matroid is \connected" if and only if the \restricted bases-exchange graph" (the bases-exchange graph restricted to exchanges involving ...

or its invariant space Inv(V1 ⊗ V2 ⊗ . . .⊗ Vn). The quantum group Uq(g) has representations and vector spaces of invariants which generalize these, and one can also study their bases, with or without the intention of specializing to q = 1. (For simplicity, we will usually consider Uq(g) as an algebra over C(q ), and we will only occassionally mention Z[q] as a ground ring.) Lusztig’s remarkabl...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

Compression of speech from the TIMIT corpus was investigated for several transform domain methods coding near-best and best bases from cosine and wavelet packet transforms. Satisficing (suboptimizing) search algorithms for selecting near-best bases were compared with optimizing algorithms for best bases in these adaptive tree-structured transforms. Experiments were performed on several hundred ...

abstract We present a uniied framework for most of the known and a few new evaluation algorithms for multivariate polynomials expressed in a wide variety of bases including the B ezier, multinomial (or Taylor), Lagrange and Newton bases. This uniication is achieved by considering evaluation algorithms for multivariate polynomials expressed in terms of L-bases, a class of bases that include the ...