Vispārināta Ermita polinoma eksistences un unitātes nosacījumi
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Latvijas Universitāte
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Abstract
Bakalaura darbs ir veltīts vispārinātiem Ermita polinomiem, kuri apmierina interpolācijas nosacījumus α_(i,j)∙p^((j)) (t_i )=α_(i,j)∙f_i^((j)), j=(0,k-1) ̅, i=(0,n) ̅, kur α_(i,j) var pieņemt vērtības 0 vai 1. Šāda tipa nosacījumi dod iespēju interpolēt funkciju gadījumā, kad mezglu punktos nav dotas visas pēc kārtas funkcijas vērtības vai tās atvasinājuma vērtības. Darbā ir pamatoti vispārināta Ermita polinoma eksistences un unitātes nepieciešamie nosacījumi un pietiekamie nosacījumi. Tika apskatīti interpolācijas uzdevumu piemēri, kuros daži no nosacījumiem neizpildās.
Bachelor’s work is devoted to generalized Hermite polynomials, which satisfy the following interpolational conditions α_(i,j)∙p^((j)) (t_i )=α_(i,j)∙f_i^((j)), j=(0,k-1) ̅, i=(0,n) ̅ with α_(i,j) equals to 0 or 1. Conditions of this tipe give possibility to interpolate functions in a case when interpolation restrictions are not provided for each derivative in order. Necessary conditions and sufficient conditions for existence and uniqueness of generalized Hermite polynomial are obtained. We consider also examples when some of such conditions are not carried out.
Bachelor’s work is devoted to generalized Hermite polynomials, which satisfy the following interpolational conditions α_(i,j)∙p^((j)) (t_i )=α_(i,j)∙f_i^((j)), j=(0,k-1) ̅, i=(0,n) ̅ with α_(i,j) equals to 0 or 1. Conditions of this tipe give possibility to interpolate functions in a case when interpolation restrictions are not provided for each derivative in order. Necessary conditions and sufficient conditions for existence and uniqueness of generalized Hermite polynomial are obtained. We consider also examples when some of such conditions are not carried out.