  We demonstrate a novel technique to obtain singular-value decomposition (SVD)
of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The
presented method is based on the Golub-Kahan bidiagonalisation strategy and
does not require $t_{ijk}^{abc}$ to be stored. The computational cost of the
method is comparable to several CCSD iterations. Moreover, the number of
singular vectors to be found can be predetermined by the user and only those
singular vectors which correspond to the largest singular values are obtained
at convergence. We show how the subspace of the most important singular vectors
obtained from an approximate triple amplitudes tensor can be used to solve
equations of the CC3 method. The new method is tested for a set of small and
medium-sized molecular systems in basis sets ranging in quality from double- to
quintuple-zeta. It is found that to reach the chemical accuracy ($\approx 1$
kJ/mol) in the total CC3 energies as little as $5-15\%$ of SVD vectors are
required. This corresponds to the compression of the $t_{ijk}^{abc}$ amplitudes
by a factor of ca. $0.0001-0.005$. Further benchmarks are performed to check
the behaviour of the method in calculation of, e.g. interaction energies or
rotational bariers, as well as in bond-breaking processes.
