Linear Grammar in less than cubic time
Yes, you can.  As Dmitry explains, CYK parsing can be used to parse a linear grammar in $O(n^2)$ time, where $n$ is the length of the input word.
CYK parsing is a dynamic programming algorithm that  sets $P[l,s,R]$ to be true if $a_{s .. s+l-1}$ can be generated from the non-terminal $R$, where $a_{1..n}$ is the input word.
Note that there is a recurrence relation that can be used to compute $P[l,s,R]$ from values of the form $P[l',s',R']$ with $l'&lt;l$, in $O(1)$ time.  In particular, if we have the rule $R \to b_1\cdots b_k Q c_1 \cdots c_m$, then we should set $P[l,s,R]$ to true if $a_{s .. s+k} = b_{1 .. k}$ and $P[l-k-m,s+k,Q]$ is true and $a_{s+l-m .. s+l-1} = c_{1 .. m}$.  Do this for each rule with $R$ on the left-hand side.  If none of them sets $P[l,s,R]$ to true, set $P[l,s,R]$ to false.  This takes $O(1)$ time (treating the size of the grammar as a constant).
We repeat this for each of the entries $P[l,s,R]$.  There are $O(n^2)$ such entries (treating the size of the grammar as a constant), and each entry takes $O(1)$ time to compute, so the entire algorithm runs in $O(n^2)$ time.