In this paper, we show that this unexpected error source is the pollution effect of a summation operation in the objective function of the PCA algorithm. The summation operator brings together unrelated parts of the data into the same optimization and the result is the reduction of the accuracy...
How I can algorithmize this equation? where Δt_sup, q and t are each vector arrays. I was given this expansion as an example for Δt_sup(3): Now I know that I need to do this within a for loop to iterate values for each corresponding value of Δt_sup(i), q(i) and t(i)...
These modified algorithms are suitable for the use in interval- arithmetic. 2 Requirements on the used floating-point arithmetic Most analysis of floating point arithmetic can be done with the simple error bound x⊕y = (x +y)(1 +ε x,y ) where |ε x,y |≤ε and ε > 0 ...
An important feature of the EIFMM is a built-in error estimation of the interpolation error made by the low-rank approximation of the far-field behavior of the kernel: the algorithm selects the optimal number of interpolation points required to ensure a given accuracy for the result, leading ...
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996) Guo, F.Z., Gao, F., Qin, S.J....
n |. This would make the algorithm run in time O(nlog n). Alternatively, one could do a bucket or radix sort on the (much shorter) exponent fields of the s i , reducing the running time to O(n). The next theorem describes our results. Theorem 1. Suppose that ...
We build hidden node feature detectors by incorporating k-monotonicity checks in the partitioning step of a constructive algorithm. Propagation constraints are also used in an MLP network using gradient descent learning to limit hyperplane movement in weight space. Results for a pattern classification ...
∑ni=1P(i)H(k)i, where p(i) is a polynomial, and ∑ni=1 Hi/(i+m), where m is an integer, are given. A method to automate these results is presented. This is achieved by using Moenck’s algorithm and by exploiting the relationship between polygamma functions and harmonic numbers....
We provide an algorithm that combines tree methods with the Improved Fast Gauss Transform (IFGT). As originally proposed the IFGT suffers from two problems: (1) the Taylor series expansion does not perform well for very low bandwidths, and (2) parameter selection is not trivial and can ...
[43]. However, the error analysis of the resummation pro- cess will be introduced also here. Accordingly, the algorithm will be presented in two subsections one for the resummation process and one for error calculations. 2.1 Hypergeometric-Meijer resummation Our hypergeometric-Meijer resummation ...