Ermita vispārinātie splaini un to konstruēšana
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Latvijas Universitāte
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Abstract
Maģistra darbs ir veltīts Ermita vispārinātiem splainiem un to konstruēšanas metodēm.
Darba mērķis ir aprakstīt Ermita vispārinātos splainus, kuri apmierina interpolācijas nosacījumus. Tas dod iespēju aprakstīt Ermita splainus gadījumā, kad interpolācijas nosacījumu skaits ir atkarīgs no sadalījuma mezgla, kā arī gadījumā, kad interpolācijas nosacījumi nav uzdoti uz visiem atvasinājumiem pēc kārtas. Pie tam interpolācijas režģis var arī nesakrist ar splaina režģi.
Ermita vispārināto splainu konstruēšanai ir aprakstīta nenoteikto koeficientu metode uz Ermita interpolācijas polinomu pamata. Iegūtās formulas ir pārbaudītas testa piemēriem, veicot aprēķinus ar datorprogrammu Maple.
Atslēgvārdi: interpolācijas uzdevums, Ermita polinoms, Ermita splains.
The master’s thesis is devoted to Hermite generalized splines and the methods of its construction. The aim of the thesis is to describe Hermite generalized splines that satisfy the following interpolation conditions. The generalized splines provide the possibility to consider Hermite splines with different number of restrictions for each interpolation point and the case when interpolation restrictions are not provided for each derivative in order. Moreover, interpolation lattice may not be equal to the spline’s lattice. For Hermite splines construction, the method of undetermined coefficients on the basis of Hermite interpolation polynomials is described. The obtained results are tested via examples performing calculations in a Maple program. Key words: interpolation, Hermite polynomial, Hermite spline.
The master’s thesis is devoted to Hermite generalized splines and the methods of its construction. The aim of the thesis is to describe Hermite generalized splines that satisfy the following interpolation conditions. The generalized splines provide the possibility to consider Hermite splines with different number of restrictions for each interpolation point and the case when interpolation restrictions are not provided for each derivative in order. Moreover, interpolation lattice may not be equal to the spline’s lattice. For Hermite splines construction, the method of undetermined coefficients on the basis of Hermite interpolation polynomials is described. The obtained results are tested via examples performing calculations in a Maple program. Key words: interpolation, Hermite polynomial, Hermite spline.