Jacobi-PIA algorithm for bi-cubic B-spline interpolation surfaces

Based on the Jacobi splitting of collocation matrices, we in this paper exploited the Jacobi-PIA format for bicubic B-spline surfaces. We first present the Jacobi-PIA scheme in term of matrix product, which has higher computational efficiency than that in term of matrix-vector product. To analyze the convergence of Jacobi-PIA, we transform the matrix product iterative scheme into the equivalent matrix-vector product scheme by using the properties of the Kronecker product. We showed that with the optimal relaxation factor, the Jacobi-PIA format for bi-cubic B-spline surface converges to the interpolation surface. Numerical results also demonstrated the effectiveness of the proposed method.