  We introduce a novel construction procedure for one-dimensional
summation-by-parts (SBP) operators. Existing construction procedures for FSBP
operators of the form $D = P^{-1} Q$ proceed as follows: Given a boundary
operator $B$, the norm matrix $P$ is first determined and then in a second step
the complementary matrix $Q$ is calculated to finally get the FSBP operator
$D$. In contrast, the approach proposed here determines the norm and
complementary matrices, $P$ and $Q$, simultaneously by solving an optimization
problem. The proposed construction procedure applies to classical SBP operators
based on polynomial approximation and the broader class of function space SBP
(FSBP) operators. According to our experiments, the presented approach yields a
numerically stable construction procedure and FSBP operators with higher
accuracy for diagonal norm difference operators at the boundaries than the
traditional approach. Through numerical simulations, we highlight the
advantages of our proposed technique.
