The spline-based models are widely used in practice to estimate the term structure of interest rates from a set of observed coupon-bond prices. The most popular method can be traced back to McCulloch (1971). Assuming that the price of a bond is equal to the present value of its future coupon payments and redemption, cash flows are regressed on a set of basis functions to estimate discount funct...

The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so–called Bernstein–Bézier form of a polynomial.

This work presents a technique to compute symbolic nonlinear approximations of the amount of dynamic memory required to safely run a method in (Java-like) imperative programs. We do that for scoped-memory management where objects are organized in regions associated with the lifetime of methods. Our approach resorts to a symbolic non-linear optimization problem which is solved using Bernstein ba...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

A new class of single-valued curves in polar coordinates obtained by a transformation of a subset of rational B ezier curves into Cartesian coordinates has recently been presented in (SS anchez-Reyes, 1990), and independently considered by P.de Casteljau, who called these curves focal B ezier. These curves are trigonometric polynomials that can be represented by a basis similar to the Bernstein...

The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. Thus we obtain a generalization of some known results in polynomial rings. The second aspect i...

Algorithms are presented that enable the element matrices for the standard finite element space, consisting of continuous piecewise polynomials of degree n on simplicial elements in R, to be computed in optimal complexity O(n). The algorithms (i) take account of numerical quadrature; (ii) are applicable to non-linear problems; and, (iii) do not rely on pre-computed arrays containing values of o...

By using generating functions, which contained alternative forms, we derive identities, some new and old, for the Bernstein basis functions. Integrating these identities, we also derive combinatorial sums involving binomial coefficients. We give relations between these combinatorial sums and generating functions for special numbers, we investigate relations related to finite sums of the powers ...

In this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity an...

A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high ...