In this note, we investigate the necessity for the measure dψ being a strong distribution, which is associated with the coefficients of the recurrence relation satisfied by the orthogonal Laurent polynomials. We also...In this note, we investigate the necessity for the measure dψ being a strong distribution, which is associated with the coefficients of the recurrence relation satisfied by the orthogonal Laurent polynomials. We also give out a representation of the greatest zeros of orthogonal Laurent polynomials in the case of dψ being a strong distribution.展开更多
In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficie...In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.展开更多
基金NNSF of China (10271022, 60373093, 69973010)the NSF of Guangdong Province (021755)
文摘In this note, we investigate the necessity for the measure dψ being a strong distribution, which is associated with the coefficients of the recurrence relation satisfied by the orthogonal Laurent polynomials. We also give out a representation of the greatest zeros of orthogonal Laurent polynomials in the case of dψ being a strong distribution.
基金supported by National Natural Science Foundation of China(Grant No.10901093)National Science Foundation of Shandong Province(Grant No.ZR2013AM006)
文摘In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.
