Abstract. We develop in this paper some efficient algorithms which are essential to implementations of spectral methods on the sparse grid by Smolyak's construction based on a...
We consider the problem of sparse interpolation of a multivariate black-box polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box polynomia...
Let f ∈ Fq[x] be a polynomial of degree d ≤ q/2. It is well-known that f can be uniquely recovered from its values at some 2d points even after some small fraction of the valu...
A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like ...