| 1. | For more rigorous and precise analysis, the numerical approximations must be used.
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| 2. | This involved the numerical approximation of a number of integrals in 360 dimensions.
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| 3. | So a numerical approximation is the best that you will get.
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| 4. | This requires more choices, such as numerical approximations or the use of heuristics.
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| 5. | This motivates the study and application of numerical approximations of integrals.
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| 6. | These representations led to fast algorithms for computing numerical approximations of.
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| 7. | If you don't allow numerical approximations, then what exactly do you mean by solving?
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| 8. | Instead, numerical approximations are calculated using root-finding algorithm for polynomials.
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| 9. | *I have seen in used with other numerical approximations, particularly in quite academic contexts.
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| 10. | If a function is numerical approximation of the derivative than the usual difference quotient.
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