Given vectors $x$ and $y$ in a Hilbert space, an interpolating
operator is a bounded operator $T$ such that $Tx=y$. An 
interpolating operator for $n$ vectors satisfies the equation 
$Tx_i =y_i$, for $i=1,2,\cdots,n$.
In this article, we investigate Hilbert-Schmidt interpolation
problems for vectors $x$ and $y$ in tridiagonal algebras.