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The approximation of (5) requires first to approximate the sequence of filtering distributions.
We use this initial consensus sequence to approximate the sequence of the transmitted founder virus es).
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Both algorithms require first a forward pass which produces a set of particles and weights approximating the sequence of filtering distributions up to time n.
This staging precludes confident determination of the transmitted/founder viruses in these subjects and therefore the statement that "initial consensus sequence approximates the sequence of the founder virus es)" is not supported.
The PF approximates recursively the sequence of posterior probability measures associated to a state-space dynamic model using a finite set of weighted samples.
In effect, the combination of high-density genotypes in the CC and the genome sequences of the CC founders yield an approximate reconstruction of the sequence of each CC line as a mosaic of fragments of the founders' genomes.
Now, we consider the problem of approximating (1.5) by the sequence of finite-dimensional problems A 0, n h ( x ) + α 1 + μ 0 ∑ i = 1 N ( A i, n h ( x ) − f i, n δ ) + α x = f 0, n δ, x ∈ X n, (2.2).
More concretely, we get from, approximating by means of the sequence of projections of such Schauder basis.
Then, the convergence of the sequence of approximate solutions (obtained in Theorem 3.1) is quadratic.
The results show that the sequence of approximate solutions (u_{n}) converges monotonically.
In general, the convergence of the sequence of approximate solutions given by the monotone iterative technique is at most linear.
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