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An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown
We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial f ( x 1 ,... x n ) = Σ t j =1 c j x 1 d j , 1 ... x n d j , n ∈ C[ x 1 ,..., x n ] ( c j ≠ 0)and the number of ter...
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| Published in: | ACM communications in computer algebra 2017-03, Vol.51 (1), p.18-20 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial
f
(
x
1
,...
x
n
) = Σ
t
j
=1
c
j
x
1
d
j
, 1
...
x
n
d
j
, n
∈ C[
x
1
,...,
x
n
] (
c
j
≠ 0)and the number of terms
t
, and that we can evaluate the value of
f
(
x
1
,...,x
n
)
at any point in C
n
in floating-point arithmetic. The problem is to find the coefficients
c
1
, ...,
c
t
and the exponents
d
1,1,
..., d
t,n
. We propose an efficient algorithm to solve the problem. |
|---|---|
| ISSN: | 1932-2240 |
| DOI: | 10.1145/3096730.3096734 |