Automatic Differentiation: Point and Interval Taylor Operators

نویسندگان

  • James B. Walters
  • George F. Corliss
چکیده

Frequently of use in optimization problems, automatic diierentiation may be used to generate Taylor coeecients. Specialized software tools generate Taylor series approximations, one term at a time, more eeciently than the general AD software used to compute (partial) derivatives. Through the use of operator overloading, these tools provide a relatively easy-to-use interface that minimizes the complications of working with both point and interval operations.

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

Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming

An introduction to both automatic differentiation and object-oriented programming can enrich a numerical analysis course that typically incorporates numerical differentiation and basic MATLAB computation. Automatic differentiation consists of exact algorithms on floating-point arguments. This implementation overloads standard elementary operators and functions in MATLAB with a derivative rule i...

متن کامل

Taylor Model Based Verified Integration for the Volterra Equations and the Lorenz System

One of the important fields in validated methods is solving initial value problems in ordinary differential equations (ODEs). The typical problem of overestimation in interval arithmetic is mostly caused by the lack of information of functional dependency. The dependency problem that is related to cancellation is one issue to be overcome. Besides, in the case of solving a system of multidimensi...

متن کامل

Estimates of Norm and Essential norm of Differences of Differentiation Composition Operators on Weighted Bloch Spaces

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.

متن کامل

ATOMFT: Solving ODES and DAEs Using Taylor Series

Taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long Taylor series. The series terms are generated recursively using the techniques of automatic differentiation. The ATOMFT system includes a translator to transform statements of the system of ODES into a FORTRAN 77 object program that is com...

متن کامل

On convergence of certain nonlinear Durrmeyer operators at Lebesgue points

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...

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 2009