solitons/ pulse propagation problemsnonlinear mediadissipationnonlinear effectsnonlinear acousticslinear approximationacoustic wavesnonlinearity dispersion relationshipsIt seems obvious that the manifestation of
Note also that λk provides an approximation for the solution of the dual problem (see for example, Problems 9.1 and 9.2). • Step 2: Stop if the primal and dual values of the objective functions are approximately equal. Else set k=k+1 and repeat from step 1. Note that in step 2...
If one simply wants one example of a solution to the problem, the choice of a priori information is unimportant. However, if one wants to develop arguments that depend on the uniqueness of the estimates, the validity of the a priori assumptions is of paramount importance. These problems are ...
\({{{\mathcal{H}}}(q)\) is a diagonal matrix whose (i, i) entry is a linear finite-impulse response (FIR) approximation of the HRF in region i, parameterized as in equation (8b) (q−1 is the standard delay operator, such that q−1x(t) = x(t − 1), see...
So in real life, of course, the expression that you're going to use the linear approximation on isn't necessarily itself linear. It can be any physical quantity. So in this case it's v squared over c squared. And now the approximation formula says that if this is approximately equal to...
b We depict an example of a linear optical circuit, for the approximation scheme with additive-error. Using s-PQDs for the linear optical circuit, one can significantly reduce the negativity bound by appropriately choosing γ < 0. c Approximation scheme with multiplicative error. When the ...
Although optimization problems for GLMs, such as logistic and Poisson regression models, are generally solved by linear approximation, Ohishi et al. (2022) and Yamamura et al. (2023) directly minimize coordinate-wise objective functions and derive update equations of a solution in closed form. ...
so this is a reasonable approximation to make (also a problem occurs with finding integer values which satisfy (for example) St-1,t=0.89It-1,t-1 unless this is assumed). If we want to ensure that demand is met from the oldest stock first then we can conclude that this is alrea...
This example shows how to compare the relationship between autoregressive modeling and linear prediction. Linear prediction and autoregressive modeling are two different problems that can yield the same numerical results. In both cases, the ultimate goal is to determine the parameters of a linear ...
Along with other problems, such systems occur in the numerical solution of partial differential equations. A good example is our discussion of a finite difference approach to the heat equation in Chapter 12. In that problem, it is necessary to solve a large tridiagonal system of equations, and...