| • | What is the Numerical Mathematics Consortium? |
| The Numerical Mathematics Consortium is an organization whose members share a common commitment to numerical algorithm development through open mathematical semantics standardization. The Numerical Mathematics Consortium will focus on the areas of core mathematical definitions, algorithm reuse, and function semantics.
DETAILS:
What are the focus areas?
The key numerical mathematics classes that will be the focus are:
| APPROXIMATION |
Approximation, Integration and Interpolation perform estimation calculations. |
| BOOLEAN |
Boolean functions manipulate the Boolean content of variables. |
| COMPARISON |
Relational operators compare numbers and matrices. |
| ELEMENTARY |
Elementary functions consist of exponential, trigonometric, and other special functions. |
| LINALGEBRA |
Linear algebra functions encapsulates the manipulation of real and complex matrices. |
| MATHCONSTANTS |
Math Constants reference known mathematical data type states useful in manipulating and evaluating expressions. |
| MATRIXGEN |
Matrix generation reference special matrix structures and content. |
| MATRIXOPS |
Matrix operators generate new matrices using unitary and binary matrix functions. |
| MEMBERSHIP |
Membership functions determine if elements belong to a given class of objects. |
| POLYNOMIALS |
Polynomial functions generate or manipulate polynomials and polynomial roots. |
| SETOPS |
Set operators manipulate groups of numeric data. |
| SPECIAL |
Special Functions compute Airy, Bessel, beta, elliptic, and other functions. |
| STATISTICS |
Statistic functions facilitate statistical analysis. |
| VECTOR ANALYSIS |
Vector Analysis produce vectors from vectors or matrices. |
The top five are:
- ELEMENTARY and SPECIAL FUNCTIONS
- APPROXIMATIONS
- LINEAR ALGEBRA
- MATRIX OPERATORS
- VECTOR ANALYSIS
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| • | Who is in the Numerical Mathematics Consortium? |
| The Numerical Mathematics Consortium is a group of mathematics vendors, researchers in academia and industry, and end users committed to eliminating this unnecessary reworking of algorithms. Current founding vendor members include:
Please visit the Member List portion of this site for a more complete list of members. |
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| • | Why is there a need for the Numerical Mathematics Consortium? |
| The Numerical Mathematics Consortium will standardize the semantics of common mathematical functions. The goal of the Numerical Mathematics Consortium is to reduce the overall cost of numerical algorithm development in different disciplines. By standardizing the function semantics, inputs and outputs will have the same meaning in any compliant application. Developers will have an easier time moving algorithms across platforms (for example, from a desktop PC to an embedded device) during a development cycle.
DETAILS:
Numerical algorithms form the backbone of many technical pursuits. From advanced research projects to industrial applications, algorithms provide the brains to problem-solving engines. Many engineers, scientists, and researchers spend months, years, or even entire careers developing and honing algorithms in efforts to provide breakthrough innovation or create a better world around us.
It is this huge investment in intellectual property that the Numerical Mathematics Consortium seeks to preserve by standardizing on a core set of mathematical functions applicable to numerical algorithms. With so much value placed in numerical algorithms, it is critical to allow the work of these technical professionals to be maintained across platforms, tools, and environments, without spending a significant amount of valuable time in “porting” or re-developing them.
Benefits:
- By standardizing the semantics of functions, inputs and outputs will have the same meaning in any compliant application.
- Developers will have an easier time moving algorithms across platforms during a development cycle.
- Empowers users to choose the best tool for a particular problem and mix and match tools without worrying about all the difficulties of learning a new product.
- Vendors can retain their intellectual property without having to conform to a specific implementation, as well as keep the advantages their individual environments provide for specific application domains.
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| • | What specific problems does the standard intend to address? |
| As modern numerical programming languages have replaced FORTRAN as the language of choice, and as new interactive design and development tools were introduced over the years, the standardized representation of common functions began to disperse again. The standard will address issues with portability, consistency, usability and functionality, and will synchronize with current standards.
DETAILS:
- Portability, consistency, and usability
The Numerical Mathematics Consortium will offer a set of function classes and functions, including parameter definitions and algorithm specifics (when appropriate). The cost to maintain algorithms across educational, research, development, prototype, and deployment disciplines will be reduced significantly. The sharing of algorithms among a community of users, disciplines, and platforms will also increase
- Standard core math functionality focus
The Numerical Mathematics Consortium will focus almost entirely on core functionality. The consortium will identify function classes and functions based on the most common functionality and usage available today. That will allow many vendors to comply with specifications published by the consortium. Classes of functions that are limited to a specialized audience will not be included in the core specification.
- Universal numerical math functionality through well-specified semantics
By focusing on the semantics of math functions, the consortium will be able to propose a universal numerical math environment. Abstracting the syntax will be beneficial to all members of the consortium and to users as well. All consortium members will still have all degrees of freedom to implement a specific instance of a function. Moreover, focusing on semantics, including definitions and references to algorithms, will reduce the overall cost of numerical algorithm development. Users will have to learn the meaning of specific functions and their parameter definition only once.
- Platform independence
Numerical algorithms are very important for a growing number of applications. They are found in mathematical packages running on standard operating systems, as part of engineering software solutions, even in office packages (spreadsheets, for example) and a growing number of embedded systems that rely heavily on numerical algorithms. All of these applications will benefit from a platform-independent definition of numerical mathematics. That is true for both horizontal compatibility (for example, among mathematics packages) and vertical compatibility (for example, mathematical packages mapped onto embedded platforms). The latter would allow developers of embedded systems to use standard mathematics packages very early in the design cycle without experiencing a paradigm shift when the transition from pure software solutions to hardware centric implementations happens.
- Synchronization with existing/de facto standards
Many core functions are related to existing IEEE standards or de facto standards such as LAPACK. Typically, existing math packages refer to and use these standards. The consortium will seek to protect these investments by making the integration of existing packages easy. For example, the semantics of linear algebra functions will be defined in such a way that the mapping onto LAPACK is straightforward and easy.
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| • | What is the history of the Numerical Math Consortium? |
| During 2004 and early 2005, a number of customers and math vendors expressed an interest in standardizing on numerical mathematics to enable portability of algorithms. An initial working group put together a draft technical scope and charter document that received good reactions from both the vendor and user communities. This group has evolved into a formal working group, the Numerical Mathematics Consortium, with the purpose of promoting standardization of core numerical mathematics. Consortium membership is open to users and vendors interested in these issues. Those interested in joining the consortium can contact any member companies or the consortium itself.
This page has more information about the history of the NMC. |
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| • | What are the next steps for the Numerical Mathematics Consortium? |
| Numerical Mathematics Consortium members will meet to review the core numerical mathematics function list and then work on semantic representations of these functions, which will be incorporated in the Numerical Mathematics Consortium specification. Compliance and validation will be focused on next, and progress will be maintained on new specifications and other associated utility and quality assurance mechanisms.
DETAILS:
At appropriate times, focused working groups will be formed to address specific technical issues, such as:
- Identifying the complete list of functions and function categories
- Developing specifications for semantics of the core functions
- Defining compliance and validation procedures
- Establishing mechanisms for reporting compliance issues
- Developing specifications for adjacent areas to the core
- Facilitating portability of Numerical Mathematics Consortium-compliant algorithms between applications
- Investigating error propagation
This page has more information about the future of the Numerical Mathematics Consortium. |
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| • | Are there other standard bodies involved or supporting this effort? |
| Numerical Mathematics Consortium members recognize ongoing efforts by other standards groups regarding mathematics. The consortium will identify key personnel to act as liaisons to these standards bodies to encourage cooperation and compatibility where possible by providing technical information and feedback. The key organizations identified at this time include:
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| • | Is the Numerical Mathematics Consortium open to new membership? How can I become involved? |
| Yes. The consortium is open to companies and individuals who support numerical algorithm development through open mathematical semantics standardization. Please visit the Membership page on this website for more information about becoming involved. |
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| • | Is there a draft standard available for review? |
| Yes. You can download the latest draft standard from the downloads section of this website. |
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| • | Who are the spokespeople I can contact for comment? |
| Any of the Marketing Contacts from the list of Full Member organizations found here can act as an NMC spokesman.
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