  Rectangular spectral collocation (RSC) methods have recently been proposed to
solve linear and nonlinear differential equations with general boundary
conditions and/or other constraints. The involved linear systems in RSC become
extremely ill-conditioned as the number of collocation points increases. By
introducing suitable Birkhoff-type interpolation problems, we present
pseudospectral integration preconditioning matrices for the ill-conditioned
linear systems in RSC. The condition numbers of the preconditioned linear
systems are independent of the number of collocation points. Numerical examples
are given.
