The truncation error
at each nodal point is given by
Extract [??] = diag([[summation].sub.11], [[summation].sub.22], [[summation].sub.kk]) (first largest k singular values) with [[summation].sub.(k+1)(k+1)] - [[epsilon].sub.rec][[summation].sub.11] < [[summation].sub.kk], where [[epsilon].sub.rec] is a relative truncation error
to control the content of recompression.
There are little computational differences at higher frequencies, which may be due to the frequency-independent approximation of the impedance Zs or the larger operating wavelength, the larger truncation error
where p is the order of the linear multistep method, O([h.sup.p+1]) is the local truncation error
, and [C.sub.p] is defined as
where the truncation error
[R.sub.i] and r are given by (3.2) and (3.5) respectively.
Stability and local truncation error
of the NSFD scheme are examined in Section 3.
[P.sub.ij] and [Q.sub.ij] are N x N matrices, O is the zero matrix, [bar.Y] = [(h[y'.sub.0], [y.sub.1], ..., [y.sub.N-1], h[y'.sub.1], ..., h[y'.sub.N]).sup.T], F = [(h[f'.sub.0]), [f.sub.1], ..., [f.sub.N-1], h[f'.sub.1], ..., h[f'.sub.N]).sup.T], C is a vector of constants, and L(h) is the truncation error
vector of the formulas in (24) and 4.
The output signal of the LUT method was affected by the truncation error
due to the limited data depth .
In addition, the stage of updating the rotation vector has the truncation error
Similar to the proof of the Theorem 2, the truncation error
of formula (40) is given by following theorem.
Bounds for truncation error
in sampling expansions of finite energy band-limited signals.