Mark the Phonemes in His / Her Repertory Bilabial Labiodental Dental Alveolar Plosive p b t [??] Nasal m [??] n Trill B r Tap / Flap [??] r Fricative [phi] [beta] f v [theta] [??] s z [??] 3 Lateral Fricative [??] [??] Approximant
[??] [??] Lateral Approximant
l Bilabial Post Alveolar Retroflex Palatal Velar Uvular Plosive t [??] [??] k g q g Nasal [eta] [??] [??] N Trill [??] Tap / Flap [??] Fricative [??] x [??] [??] Lateral Fricative Approximant
[??] j [??] Lateral Approximant
[??] [lambda] L Bilabial Pharyngeal Glottal Plosive [??] 7 Nasal Trill Tap / Flap Fricative h [??] h h Lateral Fricative Approximant
(*) In the table above the sounds/phonemes In green are the target sounds that the child is expected tc articulate.
In the context of approximating expressions of the form f(A)b for some vector b [member of] [R.sup.n], Druskin, Knizhnerman, and Simoncini [7, 16] have shown that it may be possible to approximate such an expression more accurately when using an approximant
from an extended Krylov subspace
We should use some approximations using approximation of error function and Pade approximant
as shown in the following sections.
For each [lambda] > 0, the operator [T.sub.[lambda]] : X [right arrow] [X.sup.*], defined by [T.sub.[lambda]]x = [([T.sup.-1] + X[J.sup.-1]).sup.- 1]x, is the "Yosida approximant
" of T.
has become by far the most widely used one in calculation of exponential function or formal power series due to the following reasons: first, the series may converge too slowly to be of any use and the approximation can accelerate its convergence; second, only few coefficients of the series may be known and a good approximation to the series is needed to obtain properties of the function that it represents .
In  was presented a procedure to apply Pade method to find approximate solutions for nonlinear differential equations, which consist in that the solution of a differential equation can be directly expressed as a rational power series of the independent variable as a Pade approximant
. From (6) ODP employs a polynomial-like rational expression as the proposal of approximation of the nonlinear differential equation to be solved.
Ponciano, Pade approximant
approach to the Thomas-Fermi problem, Phys.
The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pade approximant
For numerical results see Tables 4 and 6 while Figure 4 displays the approximant
and the maximum errors as compared with the results from the literature .