Triangular array: Difference between revisions

Revision as of 07:00, 16 January 2014

Revision as of 22:35, 12 February 2014

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Apart from the representation of [[triangular matrix|triangular matrices]], triangular arrays are used in several [[algorithm]]s. One example is the [[CYK algorithm]] for parsing [[context-free grammar]]s, an example of [[dynamic programming]].<ref>{{citation|title=Handbook of Natural Language Processing, Second Edition|editor1-first=Nitin|editor1-last=Indurkhya|editor2-first=Fred J.|editor2-last=Damerau|publisher=CRC Press|year=2010|isbn=9781420085938|page=65|url=http://books.google.com/books?id=nK-QYHZ0-_gC&pg=PA65}}.</ref>

[[Romberg's method]] can be used to estimate the value of a [[definite integral]] by completing the values in a triangle of numbers.<ref>{{citation|last=Thacher, Jr.|first=Henry C.|title=Remark on Algorithm 60: Romberg integration|journal=Communications of the ACM|volume=7|pages =420–421|monthdate=July|year= 1964|url=http://portal.acm.org/citation.cfm?id=364520.364542|doi=10.1145/364520.364542|issue=7}}.</ref>

The [[Boustrophedon transform]] uses a triangular array to transform one [[integer sequence]] into another.<ref>{{citation