Applicability of standard forward column/row recurrence equations for ALFs

Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.

创新型摄影测量教学实验系统的设计

为了在测绘学科教学实践中提高学生的理论水平和分析解决问题的能力,该文以摄影测量的生产流程为主线,研究实现从航空数据获取、像控点测量、空中三角测量、"4D"数据产品生成、三维建模与仿真到GIS属性入库的全过程模拟,旨在解决摄影测量课程教学过程中所面临的抽象、枯燥、高成本、高风险的问题;并以摄影测量实验系统采集的数据为基础,增加了控制测量、GIS入库、三维GIS等实验内容,以期为测绘学科的教学发展以及学生的实践能力提高作出贡献。