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Furthermore, the state-feedback gain matrices are given by 1. jj KYZjS − =, ∈ (13) Proof: From (12) and (13), we have 1 (2) 0 0 T ik ik j k ijk k kkk kij T k ZZ AZBKZPSPP Z μπ ⎡ ⎢ ⎢ − ⎢,, ⎢, ⎢ ...
An incomplete cholesky decomposition calculates Z where K= ZZ' K being the kernel matrix. Since the rank of a kernel matrix is usually low, Z tends to be smaller then the complete ...
... o=oyo=ox 0 zo=oyzo=ox 00 o=ox 10 00 o=oy 01 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 u¼B*d e ð8Þ For free vibration of laminated composite plates, the strain energy of the element is given by U e ¼ 1 2 X n k¼1 Z h kþ1 h k ZZ T * ...
kzz = (k.*zz)'; va = kzz*zz + 1.0E-4*eye(q); vb = kzz*y; a = inv(va)*vb; ss = ss + (y(i) - zz(i,:)*a)^2; end;
use an incomplete cholesky decomposition to calculate a decomposed form Z of the kernel Matrix K (where K = ZZ') and perform the calculations with Z.
With the above assumptions, equation (4) becomes * (*) ¼2 a x 2 (1** 2) Z d 3 k S xx (k) B 2 0; Z 1 0 cos (*) (k;*) e v=k k þk 2? xx þk 2 k zz ** * d*: ð10Þ For simplicity we can further assume (k ...
... of the element becomes V e ¼ P n k¼1 R h kþ1 h k RR ½r 0 x ðow=ox Þ 2þ r 0 y ðow=oy Þ 2 n þ2 s 0 xy ðow=ow*ow=oy Þ*dxdy o dz ð11Þ The kinetic energy is given by T e ¼ 1 2 X n k¼1 Z h kþ1 h k ZZ ½qð ...
An incomplete cholesky decomposition calculates Z where K= ZZ' K being the kernel matrix. Since the rank of a kernel matrix is usually low, Z tends to be smaller then the ...
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