An Algebraic-Geometric Method for Computing Zolotarev Polynomials — Additional Information

نویسنده

  • Georg Grasegger
چکیده

This report is an appendix to [2] providing two pieces of information in addition to the explicit computations of [2]. On the one hand we treat the problem of explicit construction of proper Zolotarev polynomials of higher degree using explicit expressions for proper Zolotarev polynomials of lower degree. In particular we show how Z6, as computed in [2], is related to Z2. Furthermore, we provide some ideas of intervals on the parameter t in which the Zolotarev polynomial of degree 5 is bounded by ±1 and attains these values at least 5 times.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Algebraic-Geometric Method for Computing Zolotarev Polynomials

Explicit expressions for Zolotarev polynomials of degree up to four have been known for long time (compare [15, 20]). One approach to compute Zolotarev polynomials is by quantifier elimination with cylindrical algebraic decomposition. In [5] this is used for computing Zolotarev polynomials up to degree 5. Challenged by Collins and Kaltofen [10] this was extended later up to degree 12 in [12]. A...

متن کامل

Zolotarev polynomials and optimal FIR filters

The algebraic form of Zolotarev polynomials refraining from their parametric representation is introduced. A recursive algorithm providing the coefficients for a Zolotarev polynomial of an arbitrary order is obtained from a linear differential equation developed for this purpose. The corresponding narrow-band, notch and complementary pair FIR filters are optimal in Chebyshev sense. A recursion ...

متن کامل

Bernoulli collocation method with residual correction for solving integral-algebraic equations

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

متن کامل

Solving the fractional integro-differential equations using fractional order Jacobi polynomials

In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra  integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, the...

متن کامل

Using an Imperialistic Competitive Algorithm in Global Polynomials Optimization (Case Study: 2D Geometric Correction of IKONOS and SPOT Imagery)

The number of high resolution space imageries in photogrammetry and remote sensing society is growing fast. Although these images provide rich data, the lack of sensor calibration information and ephemeris data does not allow the users to apply precise physical models to establish the functional relationship between image space and object space. As an alternative solution, some generalized mode...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016