296 research outputs found
The linear algebra of interpolation with finite applications giving computational methods for multivariate polynomials
Thesis (Ph.D.) University of Alaska Fairbanks, 1988Linear representation and the duality of the biorthonormality relationship express the linear algebra of interpolation by way of the evaluation mapping. In the finite case the standard bases relate the maps to Gramian matrices. Five equivalent conditions on these objects are found which characterize the solution of the interpolation problem. This algebra succinctly describes the solution space of ordinary linear initial value problems. Multivariate polynomial spaces and multidimensional node sets are described by multi-index sets. Geometric considerations of normalization and dimensionality lead to cardinal bases for Lagrange interpolation on regular node sets. More general Hermite functional sets can also be solved by generalized Newton methods using geometry and multi-indices. Extended to countably infinite spaces, the method calls upon theorems of modern analysis
Tropicalization and irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions in order to characterize the
irreducibility of the determinant of the generic Vandermonde matrix over the
algebraic closure of any field k. We also characterize those determinants whose
tropicalization with respect to the variables of a row is irreducible.Comment: 10 pages, AMSart. Revised version to appear in Proceedings of the AM
Finite element methods for space-time reactor analysis
"MIT-39-3-5."Also issued as a Sc. D. thesis by Chang Mu Kang in the Dept. of Nuclear Engineering, 1971Includes bibliographical references (leaves 147-150)AT(30-1) 390
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