پیوندهای مفید
آمار
| تعداد نشریات | 31 |
| تعداد شماره‌ها | 708 |
| تعداد مقالات | 6,651 |
| تعداد مشاهده مقاله | 9,178,842 |
| تعداد دریافت فایل اصل مقاله | 6,295,512 |
Bases for polynomial-based spaces | ||
| Journal of Mathematical Modeling | ||
| مقاله 11، دوره 7، شماره 1، خرداد 2019، صفحه 21-34 اصل مقاله (645.47 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2018.11242.1189 | ||
| نویسندگان | ||
| Maryam Mohammadi* 1؛ Maryam Bahrkazemi2 | ||
| 1Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran | ||
| 2School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran | ||
| چکیده | ||
| Since it is well-known that the Vandermonde matrix is ill-conditioned, this paper surveys the choices of other bases. These bases are data-dependent and are categorized into discretely $\ell^2$-orthonormal and continuously $L^2$-orthonormal bases. The first one is defined via a decomposition of the Vandermonde matrix while the latter is given by a decomposition of the Gramian matrix corresponding to monomial bases. A discussion of various matrix decomposition (e.g. Cholesky, QR and SVD) provides a variety of different bases with different properties. Special attention is given to duality. Numerical results show that the matrices of values of the new bases have smaller condition numbers than the common monomial bases. It can also be pointed out that the new introduced bases are good candidates for interpolation. | ||
| کلیدواژه‌ها | ||
| Polynomial interpolation؛ interpolation bases؛ monomial bases؛ duality؛ Vandermonde matrix؛ Gramian Matrix؛ matrix decomposition | ||
|
آمار تعداد مشاهده مقاله: 857 تعداد دریافت فایل اصل مقاله: 805 |
||