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Figure 3 Relative error versus M for a decomposition with approximately positive singular values.

Figure 4 Relative error versus K for a decomposition with approximately positive singular values.

K = 2M + 2. Figure 7 Relative error versus K for a decomposition with complex singular values.

In addition (40) allows also a decomposition with a linear first-order component.

Figure 6 Relative error versus M for a decomposition with complex singular values.

Figure 2 Average highest order coefficients energy E i versus iteration number for a decomposition with approximately positive singular values.

A CP decomposition is defined as a polyadic decomposition with a minimal number of rank-one terms which are needed to exactly fit a given HO array.

By recursively applying the same scheme to the LL subband a multiresolution decomposition with a desires level can then be achieved.

Wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed.

A similar decomposition with an additional dependence on λ also holds for A ˜ 2 0. We remark that proper ellipticity holds automatically if n ≥ 3.  .

To study mass loss in more advanced, later stages of decomposition in the same time span as the reciprocal litter transplant experiment, a decomposition site with expected accelerated decomposition was chosen.