Sentence examples for be approximated to arbitrary from inspiring English sources
Weierstrass's approximation theorem stating that every continuous function on a bounded interval can be approximated to arbitrary accuracy by polynomials is such an important example for this process and has been played the significant role in the development of analysis.
However, the WPDCM problem is still NP-hard and cannot be approximated to arbitrary degree.
The SPDCM problem cannot be approximated to arbitrary degree in polynomial time, unless P NP.
The proof follows from the fact that the SPDCM problem cannot be approximated to arbitrary degree in polynomial time according to Theorem 2. (square).
We have proved that these two problems are NP-hard under the deterministic correlated model, and cannot be approximated to arbitrary degree, unless P NP.
We prove that these two problems are NP-hard under the deterministic correlated model, and even cannot be approximated to arbitrary degree in polynomial time.
Note that when h tends to the infinity the phases can be approximated with arbitrary high probability.
The control propagator is therefore written (tilde {U} tau) = exp [-isum_{mu= 1}^{infty} mathbf {a}_{mu} tau cdot boldsymbol {sigma }]) and may be approximated, with arbitrary accuracy, as a unitary operator in simple exponential form.
This is based on the approximation-theoretical notion of the Kolmogorov n-width d N (F ) of a given set F ⊂ R d, which quantifies how well the set can be approximated by arbitrary N-dimensional linear subspaces of R d.
Lower and upper summation bounds L and U can be obtained such that for each state x the truncation error [ 44] (15) can be a priori bounded by a predefined error tolerance ϵ > 0. Thus, p (t ) can be approximated with arbitrary accuracy by (16) as long as the required number of summands is not extremely large.
