  The work considers the $N$-server distributed computing scenario with $K$
users requesting functions that are linearly-decomposable over an arbitrary
basis of $L$ real (potentially non-linear) subfunctions. In our problem, the
aim is for each user to receive their function outputs, allowing for reduced
reconstruction error (distortion) $\epsilon$, reduced computing cost ($\gamma$;
the fraction of subfunctions each server must compute), and reduced
communication cost ($\delta$; the fraction of users each server must connect
to). For any given set of $K$ requested functions -- which is here represented
by a coefficient matrix $\mathbf {F} \in \mathbb{R}^{K \times L}$ -- our
problem is made equivalent to the open problem of sparse matrix factorization
that seeks -- for a given parameter $T$, representing the number of shots for
each server -- to minimize the reconstruction distortion $\frac{1}{KL}\|\mathbf
{F} - \mathbf{D}\mathbf{E}\|^2_{F}$ overall $\delta$-sparse and $\gamma$-sparse
matrices $\mathbf{D}\in \mathbb{R}^{K \times NT}$ and $\mathbf{E} \in
\mathbb{R}^{NT \times L}$. With these matrices respectively defining which
servers compute each subfunction, and which users connect to each server, we
here design our $\mathbf{D},\mathbf{E}$ by designing tessellated-based and
SVD-based fixed support matrix factorization methods that first split
$\mathbf{F}$ into properly sized and carefully positioned submatrices, which we
then approximate and then decompose into properly designed submatrices of
$\mathbf{D}$ and $\mathbf{E}$.
