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
Metallic nanowire arrays （NWAs） possess wide application prospects due to their unique property, and the tailoring of NWAs＇ structure and morphology is of importance since it would significantly influence the per- ...Metallic nanowire arrays （NWAs） possess wide application prospects due to their unique property, and the tailoring of NWAs＇ structure and morphology is of importance since it would significantly influence the per- formance of NWAs. In the present work, the morphology and structure evolution of the NWAs prepared by the newly developed die nanoimprinting technique has been investigated in detail. It was found that increasing pro- cessing temperature, time and pressure could increase the length of the nanowires and change the NWAs＇ morphol- ogy from monodispersed form to aggregated form. Increasing processing time and temperature within the supercooled liquid region would promote crystallization, while increasing processing pressure could suppress the crystallization. This work provided important insights into the structure and morphology evolution, and therefore, the tailoring of metallic NWAs prepared by die nanoimprinting through adjusting the process parameters.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This work was supported by the National Natural Science Foundation of China （51271095 and 51101090）, and PhD Program Foundation of Ministry of Education of China （20120002110038）.
文摘Metallic nanowire arrays （NWAs） possess wide application prospects due to their unique property, and the tailoring of NWAs＇ structure and morphology is of importance since it would significantly influence the per- formance of NWAs. In the present work, the morphology and structure evolution of the NWAs prepared by the newly developed die nanoimprinting technique has been investigated in detail. It was found that increasing pro- cessing temperature, time and pressure could increase the length of the nanowires and change the NWAs＇ morphol- ogy from monodispersed form to aggregated form. Increasing processing time and temperature within the supercooled liquid region would promote crystallization, while increasing processing pressure could suppress the crystallization. This work provided important insights into the structure and morphology evolution, and therefore, the tailoring of metallic NWAs prepared by die nanoimprinting through adjusting the process parameters.
