This follows from the following computations: (4.17).
To show Theorem 4.2, which was used in the proof of Theorem 4.1, we need the following preliminary computations.
The following numerical computations (see Table 1) would show that (delta_{n}< a_{n}) and (b_{n}<omega_{n}) for (ninmathbb{N}).
Remark 2.5 The following numerical computations (see Table 1) would show that, for n ∈ N ∖ { 1 }, inequality (2.18) is sharper than inequality (2.6).
Then, for t ∈ [ 0, T ], and following similar computations to those in the first step, we have | u ( t ) | ≤ ψ ( ∥ u ∥ ) ∥ p ∥ Λ + Φ, which leads to ∥ u ∥ ψ ( ∥ u ∥ ) ∥ p ∥ Λ + Φ ≤ 1.
Then, for t ∈ [ 0, T ], and following similar computations to the first step, we have | x ( t ) | ≤ ψ ( ∥ x ∥ ) ∥ p ∥ Ω, which leads to ∥ x ∥ ψ ( ∥ x ∥ ) ∥ p ∥ Ω ≤ 1.
Then, for (tin[0,T]), and the following similar computations to the first step, we have bigl|x t bigr|lepsibigl(|x|bigr)|p|Lambda+Phi, which leads to frac{|x|}{psi(|x|)|p|Lambda+Phi}leq1.
This step reduces the overall number of positions in the following alignment computations and improves the taxonomic assignment of queries that have undergone genome rearrangements, resulting in a different order of these segments.
These coefficients could be computed in advance and stored for the following computations.
Separate results may be punched for each type of calculation, or the results may be stored and used as a factor for following computations.
Optimal input parameters are derived for the following matrix-based computations: matrix vector multiplication (Mv), matrix matrix multiplication (MM), and convolution.
