Bell System Technical Journal Research Articles

Advances in services, networks, and technology addressing service providers' future needs

This issue of the Bell Labs Technical Journal portrays wide variation considering several aspects. First, this issue introduces a new category of entries — letters. In contrast to the traditional papers, which continue to be a Journal staple, the letters bring technical issues and considerations to the fore through brief analysis. Second, the subject matter in this issue varies widely, including the following topics: services, multi-network management, soft-phone technology, wireless technology, and process advances. Third, the treatment style ranges from broad assessment of an area of interest to focused comparison of techniques.

Coding and Compression: A Happy Union of Theory and Practice

The mathematical theory behind coding and compression began a little more than 50 years ago with the publication of Claude Shannon's (1948) Mathematical Theory of Communication in the Bell Systems Technical Journal. This article laid the foundation for what is now known as information theory in a mathematical framework that is probabilistic (see, e.g., Cover and Thomas 1991; Verdui 1998); that is, Shannon modeled the signal or message process by a random process and a communication channel by a random transition matrix that may distort the message. In the five decades that followed, information theory provided fundamental limits for communication in general and coding and compression in particular. These limits, predicted by information theory under probabilistic models, are now being approached in real products such as computer modems. Because these limits or fundamental communication quantities, such as entropy and channel capacity, vary from signal process to signal process or from channel to channel, they must be estimated for each communication setup. In this sense, information theory is intrinsically statistical. Moreover, the algorithmic theory of information has inspired an extension of Shannon's ideas that provides a formal measure of information of the kind long sought in statistical inference and modeling. This measure has led to the minimum description length (MDL) principle for modeling in general and model selection in particular (Barron, Rissanen, and Yu 1998; Hansen and Yu 1998; Rissanen 1978, 1989). A coding or compression algorithm is used when one surfs the web, listens to a CD, uses a cellular phone, or works on a computer. In particular, when a music file is downloaded through the internet, a losslessly compressed file (often having a much smaller size) is transmitted instead of the original file. Lossless compression works because the music signal is statistically redundant, and this redundancy can be removed through statistical prediction. For digital signals, integer prediction can be easily done based on the past signals that are available to both the sender and receiver, and so we need to transmit only the residuals from the prediction. These residuals can be coded at a much lower rate than the original signal (see, e.g., Edler, Huang, Schuller, and Yu 2000).

On the M/G/1 Bernoulli feedback queue with multi-class customers

We consider an M/G/1 queue with Bernoulli feedback policy and multi-class customers. We assume that different classes of customers have different arrival rates, service time distributions and feedback parameters. We obtain the joint probability generating function of system size of each class and also obtain the Laplace–Stieltjes transform of the total response time of a customer in each class. Using these results we obtain the moments of system size of each class and total response time of a customer in each class. Scope and purpose We obtain the joint distribution of system size of each class and distribution of total response time of a customer in each class for M/G/1 Bernoulli feedback queue with multi-class customers which has been an open problem since Takacs, Bell System Technical Journal 1963;42:509–19, analyzed the classical M/G/1 Bernoulli feedback queue with single-class customers. We also obtain the mean and higher moments of the system size of each class and total response time for a customer in each class.

Bell Labs innovation briefs

Bell Labs Technical JournalVolume 1, Issue 1 p. 146-147 Bell Labs innovation briefs First published: Spring 1996 https://doi.org/10.1002/1538-7305(199622)1:1<146::AID-BLTJ2011>3.0.CO;2-OAboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract The briefs in this section are summaries of recent Bell Labs discoveries and developments. Readers who wish to obtain further information or to contribute future items are encouraged to contact the Bell Labs Technical Journal editor. The Inferno™ Network Operating System — for Any Device, Any Network, Any Platform High-Quality Packet Telephony with Elemedia™ Software Molecular Beam Epitaxy Using Solid Phosphorus 10 Gb/s Transmission Experiment Fiber Transmission with 1 Tb/s Capacity Volume1, Issue1Special Issue: Two-Way Broadband Access NetworksSpring 1996Pages 146-147 RelatedInformation

Database Systems: Database Work at Bell Laboratories

This computing issue of The Bell System Technical Journal is devoted to papers discussing some of the many database applications at Bell Laboratories. This paper introduces the themes described more fully in the other papers in the issue.

A Comparison of Three Speech Coders to be Implemented on the Digital Signal Processor

The recently developed digital signal processor is a device used for implementing low- to medium-complexity speech coders. It is currently being used in implementing adaptive differential pulse-code modulation (ADPCM) coding, two-band sub-band coding, and four-band sub-band coding. This study was performed to determine optimal parameter values for the two sub-band coders in preparation for their implementation on the digital signal processor and to determine their performance relative to ADPCM. (The actual implementation of the ADPCM and two-band sub-band algorithms are discussed in other papers in Part 2 of this issue of the Bell System Technical Journal.) Performance was judged on the basis of segmental signal-to-noise ratio and a forced-choice, subjective comparison test of the coders. All three coders were simulated at bit rates of 16, 20, 24, 28, and 32 kb/s. The simulations were performed on a laboratory computer.

Digital Signal Processor: Overview: The Device, Support Facilities, and Applications

This paper introduces the DSP, a new integrated circuit for digital signal processing. We describe the capabilities of the device and the tools available for operating it. Potential applications are also discussed. The paper is an overview of those that follow in this issue of the Bell System Technical Journal.

A Conjecture on the Use of Shannon's Formula for Measuring Spatial Information

Geographical AnalysisVolume 11, Issue 3 p. 304-310 Free Access A Conjecture on the Use of Shannon's Formula for Measuring Spatial Information Michael Batty, Michael Batty Michael Batty is reader in geography, University of Reading, and adjunct professor of civil engineering. University of Waterloo.Search for more papers by this authorRoger Sammons, Roger Sammons Roger Sammons is lecturer in geography, University of Reading.Search for more papers by this author Michael Batty, Michael Batty Michael Batty is reader in geography, University of Reading, and adjunct professor of civil engineering. University of Waterloo.Search for more papers by this authorRoger Sammons, Roger Sammons Roger Sammons is lecturer in geography, University of Reading.Search for more papers by this author First published: July 1979 https://doi.org/10.1111/j.1538-4632.1979.tb00696.xCitations: 11 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED 1 Arumi, F. N. Entropy and Demography. Nature (London), 243 (1973), 497– 99. 2 Batty, M. Urban Density and Entropy Functions. Journal of Cybernetics, 4 (1974), 41– 55. 3 Batty, M., and R. Sammons. On Searching for the Most Informative Spatial Pattern. Environment and Planning A, 10 (1978), 747– 79. 4 Guiasu, S. Information Theory with Applications. New York: McGraw-Hill, 1977. 5 Hobson, A., and B. K. Cheng. A Comparison of the Shannon and Kullback Information Measures. Journal of Statistical Physics, 7 (1973), 301– 10. 6 Jaynes, E. T. Information Theory and Statistical Mechanics. Physics Review, 106 (1957), 620– 30. 7 MacQueen, J., and J. Marschak. Partial Knowledge, Entropy and Estimation. Proceedings of the National Academy of Sciences, USA, 72 (1975), 3819– 24. 8 Reyni, A. Probability Theory. Amsterdam: North-Holland, 1970. 9 Reza, F. M. An Introduction to Information Theory. New York: McGraw-Hill, 1961. 10 Sammons, R. J. A Simplistic Approach to Political Redistricting”. In Spatial Representation and Spatial Interaction, edited by I. Masser and P. Brown, pp. 71– 94. Leiden, Holland: Martinus Nijhoff, 1978. 11 Shannon, C. E. A Mathematical Theory of Communication. Bell System Technical Journal, 27 (1948), 379– 423, 623–56. 12 Soest, J. L. van. Some Consequences of the Finiteness of Information”. In Information Theory: Proceedings of the Third London Symposium, edited by C. Cherry, pp. 3– 6. London: Butterworths, 1956. 13 Sukhov, V. I. Application of Information Theory in Generalisation of Map Contents. International Yearbook of Cartography, 10 (1970), 41– 47. 14 White, H. C. The Entropy of a Continuous Distribution. Bulletin of Mathematical Biophysics (Special Issue), 27 (1965), 135– 43. Citing Literature Volume11, Issue3July 1979Pages 304-310 ReferencesRelatedInformation

The effects of ADPCM coding and LPC vocoding on an automatic speaker verification system

In an earlier report [C. A. McGonegal et al., J. Acoust. Soc. Am. 62, S4(A) (Fall 1977).] the effects of several transmission systems on speaker verification by human listeners were investigated. There it was shown that the transmission system played a significant role in the speaker verification process. In this talk we show the effects of the transmission system on an existing automatic speaker verification system [A. E. Rosenberg, Bell Systems Technical Journal 55, 723–744 (1976)] in which the measured features are pitch and gain as a function of time for a specified utterance. There were ten male and ten female customers and 40 male and 40 female imposters in this experiment. All utterances were recorded using a conventional telephone connection. Post processing included ADPCM coding and LPC vocoding. Preliminary results indicate that, on the average, the transmission system affects the verification accuracy, especially when the reference and test utterances are subjected to different transmission conditions.

UNIX Time-Sharing System: Preface

Since 1962, The Bell System Technical Journal has published over 90 articles on computer programming. Although that number is not insignificant, it is only about 6 percent of all the articles published in the B.S.T.J. during that period. publications in the B.S.T.J. tend to reflect the amount of activity in many areas of technology at Bell Laboratories, but that has certainly not been true for computer programming work. Better indicators of the importance of programming work. Better indicators of the importance of programming for current Bell Laborartories work are the following: (i) 25 percent of the technical staff spent more than 50 percent of their time on programming, or related work, in 1977. (ii) 25 percent of the professional staff recruited in 1977 majored in computer science. (iii) 40 percent of the employees entering the Bell Laboratories Graduate Study Program in 1977 are majoring in computer science.

An Ergodic Theorem for Regenerating Processes

Previous article Next article An Ergodic Theorem for Regenerating ProcessesG. P. KlimovG. P. Klimovhttps://doi.org/10.1137/1121046PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Walter L. Smith, Renewal theory and its ramifications, J. Roy. Statist. Soc. Ser. B, 20 (1958), 243–302 MR0099090 0091.30101 Google Scholar[2] G. P. Klimov, Stochastic Queuing Systems, Nauka, Moscow, 1966, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Preventive Maintenance of the k-out-of-n System with Respect to Cost-Type Criterion4 November 2021 | Mathematics, Vol. 9, No. 21 Cross Ref Upper and Lower Bounds on Mean Throughput Rate and Mean Delay in Memory-Constrained Queueing Networks29 July 2013 | Bell System Technical Journal, Vol. 62, No. 2 Cross Ref Volume 21, Issue 2| 1977Theory of Probability & Its Applications History Submitted:27 December 1974Published online:17 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1121046Article page range:pp. 392-395ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Integrated optics

The appearance of “Integrated Optics: An Introduction” by Stewart E. Miller in the September 1969 Bell System Technical Journal signalled the birth of an activity that now occupies thousands of researchers. Bell Labs, among others, had been concerned with optical communications for some time, encouraged in this activity by the advent of the laser. Miller pointed out that the then typical optical telephone repeater, involving a laser, modulator, detector, lenses, and so on, spread out on an optical bench, was a form of extremely short-range radio communication and as such suffered from a number of difficulties. The apparatus was sensitive to ambient temperature gradients, to temperature changes, to mechanical vibrations of the separately mounted parts. The elegant solution to these problems proposed by Miller was to combine the separate components on the same substrate or chip, connecting them by miniature transmission lines or waveguides. Because the size of the components need only be of the order of the wavelength of light in one, and possibly two, dimensions, the substrate could be quite small—centimeters or less. He proposed calling such an assembly of components an “integrated optical circuit,” in view of its analogy to the assembly of electrical components on an integrated circuit chip.

A Note on Finding the Shortest Spanning Tree Of a Graph by Programmable Methods

Geographical AnalysisVolume 8, Issue 2 p. 201-204 Free Access A Note on Finding the Shortest Spanning Tree Of a Graph by Programmable Methods Trevor R. Fietz, Trevor R. Fietz Trevor R. Fietz is senior lecturer in civil engineering, The University of New South Wales, Sydney, Australia.Search for more papers by this author Trevor R. Fietz, Trevor R. Fietz Trevor R. Fietz is senior lecturer in civil engineering, The University of New South Wales, Sydney, Australia.Search for more papers by this author First published: April 1976 https://doi.org/10.1111/j.1538-4632.1976.tb01068.xCitations: 1 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED 1 Bell, D. A. “The Principles of Sorting.” The Computer Journal, 1 (April, 1958, to January, 1959), 71– 77. 2 Fietz, T. R. “On Finding the Shortest Spanning Tree of a Graph.” Water Research Laboratory Report No. 134, University of New South Wales, Sydney, Australia, 1974. 3 Fietz, T. R. “A Note on Finding the Shortest Spanning Tree of an Incomplete Connected Graph by Manual Methods.” Geographical Analysis, 7 (July, 1975), 311– 14. 4 Gruenberger, F., and G. Jaffray. Problems for Computer Solution. New York: John Wiley, 1965. 5 Hyman, S. I., and R. I. Jones. “Loop Defining Techniques for Gas Distribution Networks Analysis.” American Gas Association Monthly, (February, 1967) 344– 54. 6 Loberman, H., and A. Weinberger. “Formal Procedures for Connecting Terminals with a Minimum Total Wire Length.” Journal of the Association for Computing Machinery, 4 (1957), 428– 37. 7 Obruca, A. “Algorithm Mintree.” The Computer Bulletin, 8 (1964), 67. 8 Obruca, A. “Spanning Tree Manipulation and the Travelling Salesman Problem.” The Computer Journal, 10 (1968), 374– 77. 9 Ore, O. Theory of Graphs. American Mathematical Society, 1962. 10 Prim, R. C. “Shortest Connection Networks and Some Generalizations.” The Bell System Technical Journal, 36 (1957), 1389– 1401. 11 Travers, K. “The Mesh Method of Gas Network Analysis,” Gas Journal, (November, 1967), 167– 74. Citing Literature Volume8, Issue2April 1976Pages 201-204 ReferencesRelatedInformation

The MacWilliams Identities for Nonlinear Codes

In recent years a number of nonlinear codes have been discovered which have better error-correcting capabilities than any known linear codes. However, very little is known about the properties of such codes. In this paper we study the most basic property, the weight enumerator. The weight of a codeword is the number of its nonzero components; the weight enumerator gives the number of codewords of each weight, and is fundamental for obtaining the error probability when the code is used for error-correction on a noisy channel. In 1963 one of us showed that the weight enumerator of a linear code is related in a simple way to that of the dual code (Jessie MacWilliams, “A Theorem on the Distribution of Weights in a Systematic Code,” Bell System Technical Journal, 42, No. 1 (January 1963), pp. 79–94). In the present paper, which is a sequel, we show that the same relationship holds for the weight enumerator of a nonlinear code. Furthermore, a definition is given for the dual α <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sup> of a nonlinear binary code α which satisfies (α <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sup> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sup> = α provided α contains the zero codeword.

Sputtered Glass Waveguide for Integrated Optical Circuits

A series of papers which appeared in the September 1969 issue of the Bell System Technical Journal treated the theory of dielectric waveguides and stressed the potential use of such media for optical communication circuits. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1−4</sup> Here we report on the realization of low-loss, thin glass films which can be used for circuit fabrication. Methods of preparing planar films and waveguides having rectangular cross section are described along with the techniques used in evaluating their optical characteristics.

Hao Wang. Proving theorems by pattern recognition I.Communications of the Association for Computing Machinery, vol. 3 (1960), pp. 220–234. - Hao Wang. Proving theorems by pattern recognition—II.The Bell system technical journal, vol. 40 (1961), pp. 1–41.

Hao Wang. Proving theorems by pattern recognition I.Communications of the Association for Computing Machinery, vol. 3 (1960), pp. 220–234. - Hao Wang. Proving theorems by pattern recognition—II.The Bell system technical journal, vol. 40 (1961), pp. 1–41. - Volume 32 Issue 1

The Synthesis of Certain Subclasses of Tridiagonal Matrices with Prescribed Eigenvalues

Previous article Next article The Synthesis of Certain Subclasses of Tridiagonal Matrices with Prescribed EigenvaluesIsrael NavotIsrael Navothttps://doi.org/10.1137/0115023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] L. Fox, An introduction to numerical linear algebra, Monographs on Numerical Analysis, Clarendon Press, Oxford, 1964xi+295, Chap. 10 MR0164436 0122.35701 Google Scholar[2] C. Donald LaBudde, The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations, Math. Comp., 17 (1963), 433–437 MR0156455 CrossrefGoogle Scholar[3] Ernst A. Guillemin, Synthesis of passive networks. Theory and methods appropriate to the realization and approximation problems, John wiley and Sons, Inc., New York, 1958xviii+741, Chap. 10 MR0137480 Google Scholar[4] N. Balabanian, Network Synthesis, Prentice-Hall, Englewood Cliffs, New Jersey, 1958, Chap. 3 Google Scholar[5] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948, 161–162 MR0025596 0035.03601 Google Scholar[6] G. Chrystal, Algebra, Part II, Chelsea, New York, 1952, Chap. 39 Google Scholar[7] Louis Weinberg and , Paul Slepian, Takahasi's results on Tchebycheff and Butterworth ladder networks, IRE Trans., CT-7 (1960), 88–101 MR0142304 Google Scholar[8] I. Navot, , B. Gonen and , Z. Peri, Explicit formulas for Butterworth and Chebycheff ladder filters with new patterns of reflection zeros, 1966, Proc. 4th Allerton Conference on Circuit and System Theory, University of Illinois, to appear Google Scholar[9] T. G. Marshall, Discussion of “Computer solution of the network realization problem” by D. A. Calahan, Proc. 2nd Allerton Conference on Circuit and System Theory, University of Illinois, 1964, 194–200 Google Scholar[10] T. G. Marshall, Ladder network synthesis by similarity transformation, 1965, Preprint prepared for 3rd Allerton Conference on Circuit and System Theory, Radio Corporation of America, Princeton Google Scholar[11] T. G. Marshall, Primitive matrices for doubly terminated ladder networks, 1966, Proc. 4th Allerton Conference on Circuit and System Theory, University of Illinois, to appear Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the conditions for a Hamiltonian matrix to have an eigen-value density with some prescribed characteristicsJournal of Computational and Applied Mathematics, Vol. 2, No. 4 Cross Ref Synthesis of Multiple-Feedback Active Filters29 July 2013 | Bell System Technical Journal, Vol. 52, No. 4 Cross Ref A State-Space Approach to RLCT Two-Port Transfer-Function SynthesisIEEE Transactions on Circuit Theory, Vol. 19, No. 1 Cross Ref Synthesis of RLC Ladder Networks by Matrix TridiagonalizationIEEE Transactions on Circuit Theory, Vol. 16, No. 1 Cross Ref An Application of Tridiagonal Matrices to Network SynthesisR. Yarlagadda12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 16, No. 6AbstractPDF (1049 KB) Volume 15, Issue 2| 1967SIAM Journal on Applied Mathematics History Submitted:30 December 1965Published online:13 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115023Article page range:pp. 241-251ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

The spacecraft power supply system : Bomberger, D. C., D. Feldman, D. E. Trucksess, S. J. Brolin and P. W. Ussery, Bell System Technical Journal, July, 1963, 29 pgs.

The spacecraft power supply system : Bomberger, D. C., D. Feldman, D. E. Trucksess, S. J. Brolin and P. W. Ussery, Bell System Technical Journal, July, 1963, 29 pgs.

An Experimental 224 Mb/s Digital Repeatered Line

An experimental digital repeatered line has been developed which transmits information at a rate of 224 Mb/s as part of an experimental highspeed digital transmission system. The PCM terminals and time division multiplex portions were described by J. S. Mayo and others in the November 1965 issue of the Bell System Technical Journal. The repeatered line is described in this paper. The performance of this line is shown to be suitable for coast-to-coast operation. The line utilizes 0.270-inch copper coaxial transmission lines and regenerative repeaters at one-mile intervals. Ten repeaters have been operated in tandem to form ten miles of repeatered line. Each repeater uses 25 transistors, most of them a new germanium design with a cutoff frequency, f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> , of 4 GHz. Esaki diodes provide the decision thresholds for the regeneration. Power to the repeaters is supplied by dc over the center coaxial conductor. The pulse transmission code is paired selected ternary (PST).

On the Product Form of Inverses of Sparse Matrices

Previous article Next article On the Product Form of Inverses of Sparse MatricesR. P. TewarsonR. P. Tewarsonhttps://doi.org/10.1137/1008066PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] George B. Dantzig and , Wm. Orchard-Hays, The product form for the inverse in the simplex method, Math. Tables and Other Aids to Computation, 8 (1954), 64–67 MR0061469 0055.35103 CrossrefGoogle Scholar[2] D. M. Smith and , W. Orchard-Hays, R. L. Graves and , P. Wolfe, Computational efficiency in product form L. P. codesRecent Advances in Mathematical Programming, McGraw-Hill, New York, 1963, 211–218 Google Scholar[3] Philip Wolfe and , Leola Cutler, Experiments in linear programmingRecent advances in mathematical programming, McGraw-Hill, New York, 1963, 177–200 MR0155682 0223.90001 Google Scholar[4] L. J. Larson, A modified inversion procedure for product form of inverse in linear programming codes, Comm. 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Wolfe, An algorithm for scaling matrices, SIAM Rev., 4 (1962), 142–146 10.1137/1004032 MR0137587 0108.12401 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A survey of direct methods for sparse linear systems23 May 2016 | Acta Numerica, Vol. 25 Cross Ref A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space DimensionsApplied Mathematics, Vol. 07, No. 11 Cross Ref Robust and Efficient Multifrontal Solver for Large Discretized PDEs Cross Ref Packed data structure and supersparsity savings in a linear programming codeComputers & Industrial Engineering, Vol. 18, No. 4 Cross Ref Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processorsMathematics and Computers in Simulation, Vol. 29, No. 1 Cross Ref Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 Cross Ref Analysis of programs of certain computational algorithms realized on a large-block model machineJournal of Soviet Mathematics, Vol. 10, No. 5 Cross Ref A survey of sparse matrix researchProceedings of the IEEE, Vol. 65, No. 4 Cross Ref On solving problems with sparse matricesJournal of Soviet Mathematics, Vol. 7, No. 1 Cross Ref Pivoting-order computation method for large random sparse systemsIEEE Transactions on Circuits and Systems, Vol. 21, No. 2 Cross Ref Some Experiments on Sparse Sets of Linear Equations12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 25, No. 2AbstractPDF (673 KB)A Survey of Indexing Techniques for Sparse MatricesACM Computing Surveys, Vol. 5, No. 2 Cross Ref References Cross Ref A probabilistic approach to optimal pivoting and prediction of fill-in for random sparse matricesIEEE Transactions on Circuit Theory, Vol. 19, No. 4 Cross Ref Updated triangular factors of the basis to maintain sparsity in the product form simplex methodMathematical Programming, Vol. 2, No. 1 Cross Ref A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS Cross Ref On Optimal-Pivoting Algorithms in Sparse MatricesIEEE Transactions on Circuit Theory, Vol. 19, No. 1 Cross Ref Statistical Circuit Design: Nonlinear Circuits and Statistical Design29 July 2013 | Bell System Technical Journal, Vol. 50, No. 4 Cross Ref Computations with Sparse Matrices18 July 2006 | SIAM Review, Vol. 12, No. 4AbstractPDF (1825 KB)Some results on sparse matrices1 January 1970 | Mathematics of Computation, Vol. 24, No. 112 Cross Ref On computing generalized inversesComputing, Vol. 4, No. 2 Cross Ref On the orthonormalization of sparse vectorsComputing, Vol. 3, No. 4 Cross Ref On the Chebyshev solution of inconsistent linear equationsBIT, Vol. 8, No. 3 Cross Ref Solution of linear equations with coefficient matrix in band formBIT, Vol. 8, No. 1 Cross Ref On the transformation of symmetric sparse matrices to the triple diagonal formInternational Journal of Computer Mathematics, Vol. 2, No. 1-4 Cross Ref A Direct Method for Generalized Matrix Inversion14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 4, No. 4AbstractPDF (817 KB)Solution of a system of simultaneous linear equations with a sparse coefficient matrix by elimination methodsBIT, Vol. 7, No. 3 Cross Ref The Product Form of Inverses of Sparse Matrices and Graph Theory18 July 2006 | SIAM Review, Vol. 9, No. 1AbstractPDF (962 KB) Volume 8, Issue 3| 1966SIAM Review History Submitted:17 September 1965Accepted:20 January 1966Published online:18 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1008066Article page range:pp. 336-342ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics