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304:: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).
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690:{\displaystyle \{{\sqrt {2}}\sin(2\pi nx)\mid n\in \mathbb {N} \}\cup \{{\sqrt {2}}\cos(2\pi nx)\mid n\in \mathbb {N} \}\cup \{1\}}
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The monomial basis also forms a basis for the vector space of
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on a bounded domain. As a particular example, the collection
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may be too technical for most readers to understand
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396:. After all, every polynomial can be written as
371:{\displaystyle \{x^{n}\mid n\in \mathbb {N} \}.}
526:, which is a linear combination of monomials.
281:can be represented as a linear combination of
277:of basis functions, just as every vector in a
273:in the function space can be represented as a
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64:Learn how and when to remove these messages
820:(2nd ed.). MIT Press. p. 1141.
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241:Learn how and when to remove this message
176:Learn how and when to remove this message
160:, without removing the technical details.
121:Learn how and when to remove this message
84:This article includes a list of general
27:Element of a basis for a function space
818:Encyclopedic Dictionary of Mathematics
158:make it understandable to non-experts
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296:, basis functions are also called
90:it lacks sufficient corresponding
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519:{\displaystyle n\in \mathbb {N} }
45:This article has multiple issues.
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53:or discuss these issues on the
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388:Monomial basis for polynomials
324:basis for the vector space of
261:is an element of a particular
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561:square-integrable functions
205:to comply with Knowledge's
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860:Numerical linear algebra
300:because of their use in
218:may contain suggestions.
203:may need to be rewritten
788:Finite-elements (bases)
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845:Numerical analysis
803:Numerical analysis
773:Orthogonal wavelet
697:forms a basis for
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212:You can help
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47:Please help
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718:Hamel basis
553:orthonormal
394:polynomials
255:mathematics
103:introducing
839:Categories
810:References
734:Dual basis
111:March 2013
86:references
50:improve it
676:∪
665:∈
659:∣
647:π
638:
622:∪
611:∈
605:∣
593:π
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551:form an (
509:∈
498:for some
463:⋯
355:∈
349:∣
216:talk page
56:talk page
707:See also
322:monomial
308:Examples
271:function
269:. Every
152:Please
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747:in an
726:(in a
537:": -->
265:for a
214:. The
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263:basis
257:, a
822:ISBN
761:and
559:for
539:edit
320:The
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581:sin
288:In
253:In
156:to
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359:N
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