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REPORTS > KEYWORD > INTEGRATION, INAPPROXIMIABLITY, REDUCTION:
Reports tagged with Integration, Inapproximiablity, Reduction:
TR10-202 | 9th December 2010
Bin Fu

#### Multivariate Polynomial Integration and Derivative Are Polynomial Time Inapproximable unless P=NP

We investigate the complexity of integration and
derivative for multivariate polynomials in the standard computation
model. The integration is in the unit cube $[0,1]^d$ for a
multivariate polynomial, which has format
$f(x_1,\cdots, x_d)=p_1(x_1,\cdots, x_d)p_2(x_1,\cdots, x_d)\cdots p_k(x_1,\cdots, x_d)$,
where each $p_i(x_1,\cdots, x_d)=\sum_{j=1}^d q_j(x_j)$ with
all single variable polynomials $q_j(x_j)$ ... more >>>

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