NDLI: Computing multivariable Taylor series to arbitrary order

Please wait, while we are loading the content...

The role of dynamic programming & control structures in performance

Recycling APL code into client/server applications

Deploying complex decision technologies with APL to solve the daily output planning problem: a tale from two of the last of the Jedi Knights

Holland classifier systems

Bounded rationality and adaptive agents in economic modeling

Translation of nested APL to C++: problems and approaches

Modeling the effects of acid leaching on concrete

The philosophy of nothing and everything

Rank and uniformity

Representations of recursion

APL, dynamic programming, and the optimal control of electromagnetic brake retarders

Regression analysis with fuzzy knowledge representation

The role of composition in computer programming

Computing multivariable Taylor series to arbitrary order

Untying the Gordian knot: agreement in J

AVCS: the APL version control system

Infix, cut and finite automata

Early bankruptcy detection using neural networks

Fuzzy control of technological processes in APL2

Concrete multidimensional statistics in APL2

Namespaces: APL/W vs. APL2

Doing ANOVA calculations on the computer

An APL implementation of the Club of Rome's world model

APL is important at USAA (abstract)

A new approach for developing applications using asynchronous AP144 and synchronous AP207 (abstract)

Computing multivariable Taylor series to arbitrary order

Content Provider	ACM Digital Library
Author	Neidinger, Richard D.
Abstract	Automatic differentiation, manipulating numerical vectors of coefficients, is the efficient way to compute multivariable Taylor series. This does not require symbolic differentiation or numerical approximation but uses exact formulas applied to numerical arrays. Arrays of Taylor series coefficients of any elementary function can be built-up, as the array for each component (combination or function) is a combination of its argument arrays. The functions TIMES and EXP display the algorithmic ideas that enable all of the other standard functions. We study the interesting recursive formulas for these combinations, the resulting algorithms, and the implementation in APL. To handle all coefficients in n variables up to order m, the arrays are hyper-pyramid data structures, considered conceptually as n-dimensional but implemented as one-dimensional arrays. Unlike previous work, this implementation does not require huge arrays for binomial coefficients and indirect referencing. This APL*PLUS III implementation loops through one nested reference array and takes sub-arrays from another for a practical solution to this problem that can make tremendous demands on time and space.
Starting Page	134
Ending Page	144
Page Count	11
File Format	PDF
ISBN	0897917227
DOI	10.1145/206913.206988
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1995-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Nested arrays Taylor series Numerical method Data structure Partial derivatives Automatic differentiation
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Computing multivariable Taylor series to arbitrary order

An efficient method for the numerical evaluation of partial derivatives of arbitrary order

Computing of b-series by automatic differentiation.

Sensitivity Analysis of ODES/DAES Using the Taylor Series Method

Technical Initial Problems and Automatic Transformation

Tadiff, A Flexible C++ Package For Automatic Differentiation using Taylor series expansion (1997)

Taylor-Mode Automatic Differentiation for Higher-Order Derivatives in JAX

Data structure and algorithms for fast automatic differentiation.

From Taylor Series to Taylor Models (1997)

Computing multivariable Taylor series to arbitrary order

Similar Documents

Computing multivariable Taylor series to arbitrary order

An efficient method for the numerical evaluation of partial derivatives of arbitrary order

Computing of b-series by automatic differentiation.

Sensitivity Analysis of ODES/DAES Using the Taylor Series Method

Technical Initial Problems and Automatic Transformation

Tadiff, A Flexible C++ Package For Automatic Differentiation using Taylor series expansion (1997)

Taylor-Mode Automatic Differentiation for Higher-Order Derivatives in JAX

Data structure and algorithms for fast automatic differentiation.

From Taylor Series to Taylor Models (1997)

Computing multivariable Taylor series to arbitrary order