This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
Several results on optical-axis perturbation and elimination of the mismatching error C of a monolithic triaxial ring resonator （MTRR） are reported. Based on the augmented 5×5 ray matrix method, by simultaneous...Several results on optical-axis perturbation and elimination of the mismatching error C of a monolithic triaxial ring resonator （MTRR） are reported. Based on the augmented 5×5 ray matrix method, by simultaneously considering axial displacement of a mirror and the misalignments in three planar square ring resonators of a MTRR, the rules of optical-axis perturbation are obtained. The mismatching error C of the MTRR is eliminated. The results obtained are important for cavity design, as well as in the improvement and alignment of MTRR.展开更多
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
基金supported by the National Natural Science Foundation of China under Grant Nos.60608002and 60608002
文摘Several results on optical-axis perturbation and elimination of the mismatching error C of a monolithic triaxial ring resonator （MTRR） are reported. Based on the augmented 5×5 ray matrix method, by simultaneously considering axial displacement of a mirror and the misalignments in three planar square ring resonators of a MTRR, the rules of optical-axis perturbation are obtained. The mismatching error C of the MTRR is eliminated. The results obtained are important for cavity design, as well as in the improvement and alignment of MTRR.
