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We have no convergence proof for Alg. 2. Empirically, Alg. 2 converges, providing us with estimates of home locations for 91,984,163 Twitter users.
Then every solution of (2) converges to (overline{x}).
Therefore, the EOF series in Eq. (2) converges most quickly in representing the true height dataset.
Then e 1 and e 2 converges to zero as ( t to infty ).
On the other hand, (55) implies that α 2 converges to zero almost surely.
Furthermore, if ILC Loop 2 converges "almost" monotonically, ILC Loop 1 and ILC Loop 2 can update simultaneously to achieve uniform convergence of the overall system.
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end{aligned} where (A^) is the adjoint of A and (0<lambda<2alpha) with (alpha =frac{1}{|A|^{2}}), converges weakly to a solution of (3.9).
As f 1 is growing on [ 0,M 2], we conclude that the sequence ( σ ̂ ( i + 1 ) 2 ) converges to one of the fixed point of f 1.
To show every solution in (R_{2}) converges to (E_{0}), it is enough to consider those solutions in (operatorname{int}(Q_{4}(E^))).
Moreover, for any y0 ∈ Y, the sequence { y n } n = 0 ∞, defined by y n = Φ yn-1), n = 1, 2,..., converges to this unique fixed point.
Therefore, g t converges to a finite value, and, as a consequence of (33), the weighted norm ({| boldsymbol {z}_{t+1} - boldsymbol {z}_{t} |}_{epsilon _{infty }}^{2}) converges to 0, i.e., z t converges to a finite value too.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com