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CC BY-NC-ND V4.0, Open Access
Dissertation
Entry-wise Recursive Determination of Template Arrays
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000005434
Handle:
https://hdl.handle.net/2376/119582
Abstract
In a two-dimensional recurrence relation, there is an underlying structure composed of the two-dimensional sequences (arrays) in which the set of indices is extended from N^2 to Z^2. The recurrences have coefficients that come from a field F. We give a set of initial conditions sufficient to build a uniquely-determined array from a given recurrence and initial conditions.
Elementary arrays, arrays with initial conditions that are all zero except for one, which has a 1 in it, are shown to be linearly independent. Some of the conditions under which a Schauder basis exists for the set of arrays are determined, as well as how to construct such a basis. A Schauder basis is a sequence {x_k} with the property that each array has a unique representation of the form x=\sum_{k=1}^\infty c_k x_k for c_k in F, a field, where \sum_{k=1}^\infty c_k x_k converges. This allows for an infinite linear combination of terms to construct the array, but we show that for the space of arrays, this sum for any given cell is finite.
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Details
- Title
- Entry-wise Recursive Determination of Template Arrays
- Creators
- Jordan Broussard
- Contributors
- Matthew Hudelson (Advisor)Judith McDonald (Committee Member)Michael Tsatsomeros (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 126
- Identifiers
- 99900592058201842
- Language
- English
- Resource Type
- Dissertation