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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Formal verification of mathematical software

Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.

Sutherland, D.↗
NASA NTRS1981

Proceedings, Conference on the Computing Environment for Mathematical Software

Recent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical software.

Source record↗
NASA NTRS1978

Extending reliability: Transformational tailoring of abstract mathematical software

Methods for automatically constructing concrete executable programs from an abstract prototype program by applying transformations based on theorems of matrix algebra and on algebraic properties of programming languages are described. These methods provide a user with highly efficient programs tailored to his environment while maintaining the advantages of high reliability and low cost associated with routines from the best mathematical software libraries. Also, the transformations which produce such programs represent a formal codification of rules for writing linear algebra programs.

Boyle, J. M.↗
NASA NTRS2009

A Verification-Driven Approach to Traceability and Documentation for Auto-Generated Mathematical Software

Model-based development and automated code generation are increasingly used for production code in safety-critical applications, but since code generators are typically not qualified, the generated code must still be fully tested, reviewed, and certified. This is particularly arduous for mathematical and control engineering software which requires reviewers to trace subtle details of textbook formulas and algorithms to the code, and to match requirements (e.g., physical units or coordinate frames) not represented explicitly in models or code. Both tasks are complicated by the often opaque nature of auto-generated code. We address these problems by developing a verification-driven approach to traceability and documentation. We apply the AUTOCERT verification system to identify and then verify mathematical concepts in the code, based on a mathematical domain theory, and then use these verified traceability links between concepts, code, and verification conditions to construct a natural language report that provides a high-level structured argument explaining why and how the code uses the assumptions and complies with the requirements. We have applied our approach to generate review documents for several sub-systems of NASA s Project Constellation.

Denney, Ewen W.↗
NASA NTRS1978

A comparison of two recent approaches to machine parameterization for mathematical software

Two proposals for expressing the dependence of numerical software on the environment are examined. The approaches are briefly summarized and the differences and similarities are discussed. One proposal characterizes the dependence of the software on the machine architecture essentially in terms of the representation of floating point entities in the machine. The second characterizes the dependence of the software on the environment in terms of models both of the floating point numbers and of the behavior of the arithmetic unit of the machine.

Smith, B. T.↗
NASA NTRS1982

Geometric models, antenna gains, and protection ratios as developed for BC SAT-R2 conference software

Mathematical models used in the software package developed for use at the 1983 Regional Administrative Radio Conference on broadcasting satellites. The models described are those used in the Spectrum Orbit Utilization Program (SOUP) analysis. The geometric relationships necessary to model broadcasting satellite systems are discussed. Antenna models represent copolarized and cross polarized performance as functions of the off axis angle. The protection ratio is modelled as a co-channel value and a template representing systems with frequency offsets.

Miller, E. F.↗
NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗
NASA NTRS1992

RT-Syn: A real-time software system generator

This paper presents research into providing highly reusable and maintainable components by using automatic software synthesis techniques. This proposal uses domain knowledge combined with automatic software synthesis techniques to engineer large-scale mission-critical real-time software. The hypothesis centers on a software synthesis architecture that specifically incorporates application-specific (in this case real-time) knowledge. This architecture synthesizes complex system software to meet a behavioral specification and external interaction design constraints. Some examples of these external constraints are communication protocols, precisions, timing, and space limitations. The incorporation of application-specific knowledge facilitates the generation of mathematical software metrics which are used to narrow the design space, thereby making software synthesis tractable. Success has the potential to dramatically reduce mission-critical system life-cycle costs not only by reducing development time, but more importantly facilitating maintenance, modifications, and extensions of complex mission-critical software systems, which are currently dominating life cycle costs.

Setliff, Dorothy E.↗
NASA NTRS1996

Computer-Based Mathematics Instructions for Engineering Students

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Khan, Mustaq A.↗
NASA NTRS2006

Grayscale Optical Correlator Workbench

Grayscale Optical Correlator Workbench (GOCWB) is a computer program for use in automatic target recognition (ATR). GOCWB performs ATR with an accurate simulation of a hardware grayscale optical correlator (GOC). This simulation is performed to test filters that are created in GOCWB. Thus, GOCWB can be used as a stand-alone ATR software tool or in combination with GOC hardware for building (target training), testing, and optimization of filters. The software is divided into three main parts, denoted filter, testing, and training. The training part is used for assembling training images as input to a filter. The filter part is used for combining training images into a filter and optimizing that filter. The testing part is used for testing new filters and for general simulation of GOC output. The current version of GOCWB relies on the mathematical software tools from MATLAB binaries for performing matrix operations and fast Fourier transforms. Optimization of filters is based on an algorithm, known as OT-MACH, in which variables specified by the user are parameterized and the best filter is selected on the basis of an average result for correct identification of targets in multiple test images.

Hanan, Jay↗
NASA NTRS1984

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Kincaid, D. R.↗
NASA NTRS1984

Some mathematical tools for a modeller's workbench

The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.

Cohen, E.↗
NASA NTRS1991

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗
NASA NTRS1985

Error Free Software

A mathematical theory for development of "higher order" software to catch computer mistakes resulted from a Johnson Space Center contract for Apollo spacecraft navigation. Two women who were involved in the project formed Higher Order Software, Inc. to develop and market the system of error analysis and correction. They designed software which is logically error-free, which, in one instance, was found to increase productivity by 600%. USE.IT defines its objectives using AXES -- a user can write in English and the system converts to computer languages. It is employed by several large corporations.

Source record↗
NASA NTRS1987

Expert system development for commonality analysis in space programs

This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.

Yeager, Dorian P.↗
NASA NTRS2005

Software Template for Instruction in Mathematics

Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.

Shelton, Robert O.↗
NASA NTRS1976

Development of a methodology for classifying software errors

A mathematical formalization of the intuition behind classification of software errors is devised and then extended to a classification discipline: Every classification scheme should have an easily discernible mathematical structure and certain properties of the scheme should be decidable (although whether or not these properties hold is relative to the intended use of the scheme). Classification of errors then becomes an iterative process of generalization from actual errors to terms defining the errors together with adjustment of definitions according to the classification discipline. Alternatively, whenever possible, small scale models may be built to give more substance to the definitions. The classification discipline and the difficulties of definition are illustrated by examples of classification schemes from the literature and a new study of observed errors in published papers of programming methodologies.

Gerhart, S. L.↗