Preconditioned progressive iterative approximation for tensor product Said-Ball patches

In order to accelerate the convergence of progressive iterative approximation（PIA） for tensor product Said-Ball patches, the preconditioning technique for PIA for tensor product Said-Ball patches is studied. Firstly, the diagonally compensate reduction is used to construct the preconditioner, then combined with the properties of Kronecker, the preconditioned progressive iterative approximation（PPIA） for tensor product Said-Ball patches is exploited. To further reduce the amount of calculation and improve the stability of the algorithm, the generalized minimal residual method is employed to inexactly solve the preconditioned equations and yield the inexact version of PPIA. The convergence of the PPIA and its inexact version are analyzed. Finally, numerical results illustrate that the proposed preconditioner can greatly reduce the spectral radii of PPIA's iteration matrices, hence accelerating the convergence rate of PPIA and its inexact version. Besides, since the preconditioner can improve the spectral distri