(0, 1, … ,m - 2, m) Interpolation on the Zeros of xL(a)n-1(x)
Received:July 25, 1993  
Key Word: Birkhoff interpolation   Laguerre Polynomial   regularity.  
Fund ProjectL:Project Supported by National Natural Science Foundation of China.
Author NameAffiliation
Shi Yingguang Computing Center
Academia Sinica BeiJing 100080 
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Abstract:
      A necessary and sufficient condition for regularity of (0, 1, …, m - 2, m) in-terpolation on the zeros of xL(a)n-1(x)(a>-1 ) in a nianagealbe form is established, where xL(a)n-1(x) is the (n-1)- th Laguerre polynomial . Meanwhile, the explicit representationof the fundamental polynomials, when they exist, is given. Moreover, we show that if theproblem of (0, 1, …, m - 2, m) interpolation has an infinity of solutions then the generalform of the solutions is f0(x)+Cf1(x) with an arbitrary constant C.
Citation:
DOI:10.3770/j.issn:1000-341X.1995.03.001
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