نتایج جستجو برای: spline methods
تعداد نتایج: 1884885 فیلتر نتایج به سال:
Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...
In this paper, we propose the generalized B divided difference, with which the (k− 1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k − 2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-...
Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...
In this paper we consider quasi-interpolatory spline operators that satisfy some interpolation conditions. We give some applications of these operators constructing approximating integral operators and numerically solving Volterra integral equations of the second kind. We prove convergence results for the constructed methods and we perform numerical examples and comparisons with other spline me...
The algorithms and programs in this handy book deal almost exclusively with cubic splines. A short introduction stresses the maximum "smoothness" of "natural" splines. The next chapter reviews the numerical solution of tridiagonal linear systems by Gauss elimination and of block tridiagonal linear systems by relaxation. Chapter 3 offers programs for cubic spline interpolation with various (sepa...
The Hybrid Spline method (H-spline) is a method of density estimation which involves regression splines and smoothing splines methods. Using basis functions (B-splines), this method is much faster than Smoothing Spline Density Estimation approach (Gu, 1993). Simulations suggest that with more structured data (e.g., several modes) H-spline method estimates the modes as well as Logspline (Kooperb...
The computation schemes of spline-collocation methods for solving singular integral equations. A theoretical foundation of these two methods is obtained in space L2. In the present paper we give theoreticaly justification of the numerical schemes of spline-collocation method for solving the singular integral equations (SIE) of the following form
چکیده در سال 1959 تقریباً به دو طور همزمان دو نفر در دو نقطه ی متفاوت دنیا بر روی منحنی ها مطالعه کار کردند ، یکی از آنها peugeot کارمند و شاگرد pierre bezier بود. پیشنهادی برای شکل جدیدی از معادله منحنی ها و سطوح برای بدنه اتومبیل ارایه کرد و به دلیل کمک شایان توجه bezier به وی و معرفی سریع تر این منحنی ها در دنیای ریاضیات این منحنی ها به نام bezier نامگذاری شدند(]3 و 2[ ). الگوریتم حل این منح...
As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...
A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...
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