The approximation tensor product surface obtained by the proposed method has no limit on its degree, i.e., arbitrary degree.
Since the ionization efficiencies of oligonucleotides vary based on sequence, this method is an approximation of product abundance.
We study the effect of product approximation on the Galerkin solutions of the one-dimensional cubic Schrödinger equation.
If product approximation is applied to the numerical representation of the nonlinear terms, then the scheme is fourth-order in space in the finite difference sense.
In the vertical-fall experiments in air and water the measured forces varied to first approximation as the product of the density and the velocity squared, but only to a first approximation, leaving room to question whether a purely inertial contribution had been isolated.
In particular, the separability of the power spectrum between the base station and the mobile is investigated, and a model is proposed and validated, based on the sum of polarization pairwise Kronecker product approximation.
As a result, we can write the Padé approximation as a product of Blachke factors: begin{aligned} exp_{[n,n]} -Tz) = prod_{n} -Tzrac{z + overline{{p}_{n} }}{z+ p_{n}}.
Based on the block-triangular product approximation to a 2-by-2 block matrix, a class of hybrid preconditioning methods is designed for accelerating the MINRES method for solving saddle-point problems.
We show that by applying the Kronecker product approximation, the storage of a three-dimensional demagnetizing tensor with N6 entries can be reduced to O N2), showing a superlinear compression behavior.
The general form of the sum of channel polarization pair-wise Kronecker product approximation is proposed to be used to model the joint polarimetric angular PSD between the BS and MS. Finally, the double-directional PSD channel model is proposed and verified by comparing the cumulative distribution functions (CDFs) of the measured and modeled ergodic mutual information.
