  In the paper, we give methods of construction of dual bases for the B-spline
basis and truncated power basis. Explicit formulas for the dual B-spline basis
are obtained using the Legendre-like orthogonal basis of the polynomial spline
space presented in (Wei et al., Comput.-Aided Des. 45 (2013), 85-92) and a
connection between orthogonal and dual bases of any space given in (Lewanowicz
and Wo\'zny, J. Approx. Theory 138 (2006), 129-150). Construction of the dual
truncated power basis is performed in two phases. We start with explicit
formulas for the dual power basis of the space of polynomials. Then, we expand
this basis using an iterative algorithm proposed in (Wo\'zny, J. Comput. Appl.
Math. 260 (2014), 301-311). As a result, we obtain the dual truncated power
basis. We also present some applications of the proposed dual polynomial spline
bases and illustrative examples.
