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Section 4 provides convergence analysis of the proposed method.

Remark 4.4 Theorem 3.1 provides convergence sequence to a common point of fixed points of a Lipschitzian pseudocontractive mapping and zeros of two monotone mappings in Hilbert spaces.

It has been shown that the algorithm provides convergence even in the case when some nodes may be unstable, owing to a proper choice of the consensus weights.

The resulting spike-reducing method in combination with the proposed STD ensures an accurate positioning of steady jumps, provides convergence with mesh refinement, which was not possible for previous methods that cannot avoid the spike.

A reasonable conjecture is that the doubly Ishikawa iteration with error and the corresponding doubly Mann iteration with error are equivalent for all maps for which either method provides convergence to a fixed point.

Under correct model assumptions, their paper also provides convergence results to the MMSE estimates of trend and seasonal for iterations starting with a non-MMSE estimate of trend (or seasonal).

Admittedly, providing convergence proof of the proposed algorithm is very difficult.

In this paper, we establish a framework of the splitting method for RT/DAE and provide convergence analysis.

Several iterations of this process would provide convergence towards a more precise estimation of the implementation effort.

The complete numerical procedure and details of assigning the numerical parameters are provided; convergence of the numerical method is demonstrated by conducting grid function convergence tests.

We provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic.