ISSN:
0945-3245
Keywords:
AMS(MOS) 41A05, 14B05, 12E05
;
CR: G1.1
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We try to solve the bivariate interpolation problem (1.3) for polynomials (1.1), whereS is a lower set of lattice points, and for theq-th interpolation knot,A q is the set of orders of derivatives that appear in (1.3). The number of coefficients |S| is equal to the number of equations Σ|A q |. If this is possible for all knots in general position, the problem is almost always solvable (=a.a.s.). We seek to determine whether (1.3) is a.a.s. An algorithm is given which often gives a positive answer to this. It can be applied to the solution of a problem of Hirschowitz in Algebraic Geometry. We prove that for Hermite conditions (1.3) (when allA q are lower triangles of orderp) andP is of total degreen, (1.3) is a.a.s. for allp=1, 2, 3 and alln, except for the two casesp=1,n=2 andp=1,n=4.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01386436
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