Showing papers in "International Journal of Computer Mathematics in 1972"
TL;DR: A method of generating non-linear transformations for increasing the rate and expanding the domain of convergence of sequences is presented, which represent in a certain sense a generalization of the well-known transformations due to Shanks and are more efficient.
Abstract: A method of generating non-linear transformations for increasing the rate and expanding the domain of convergence of sequences is presented. These transformations represent in a certain sense a generalization of the well-known transformations due to Shanks, and in many cases are more efficient. The transformations would seem to have important application in computing results from formal solutions to problems in applied mathematics when these solutions are obtained in the form of series or sequences having poor convergence. An indication is also given of application to the“evaluation”of divergent formal solutions.
375 citations
TL;DR: A global algorithm which uses interval analysis techniques to recognize live variables is presented and it is shown that this algorithm can be used to solve the challenge of recognizing live variables in discrete time.
Abstract: A global algorithm which uses interval analysis techniques to recognize live variables is presented.
59 citations
TL;DR: Simple recursion formulas are presented for computing the coefficients in the Pade table of a power series f(x) and a Fortran subroutine for the computation is given in an Appendix.
Abstract: Simple recursion formulas are presented for computing the coefficients in the Pade table of a power series f(x). A Fortran subroutine for the computation is given in an Appendix, where a second subroutine for evaluating the elements for any x is also given. Two applications are mentioned. The assumption is made that the Pade table is normal.
36 citations
TL;DR: This paper discusses some of the constraints which should be placed on compiler optimization, and describes an algorithm which determines when it is safe to move expressions out of loops.
Abstract: This paper discusses some of the constraints which should be placed on compiler optimization. First, the optimized program should produce the same output as the original program and second, the optimizer should not introduce new error side effects, such as a divide-check interrupt. The latter restriction might be called the safety constraint. Once these constraints are defined, the remainder of the paper is devoted to an algorithm which determines when it is“safe”to move expressions out of loops.
24 citations
TL;DR: In this paper, methodes numeriques for i'ecoulement laminaire d'un fluide rigide viscoplastique incompressible are presented. But this method is not suitable for the case of non-linear visco-coplastiques.
Abstract: (1972). Methodes numeriques pour i'ecoulement laminaire d'un fluide rigide viscoplastique incompressible. International Journal of Computer Mathematics: Vol. 3, No. 1-4, pp. 225-255.
23 citations
TL;DR: It is shown that the BIFORE and discrete Fourier phase spectra have several analogous properties and a fast algorithm which yields the BifORE power andphase spectra in approximately N log2 N arithmetic operations is developed.
Abstract: Corresponding to the BIFORE (Binary FOurier Representation) Power spectrum, a phase spectrum is developed. The frequency content of each of the (log2 N+1) phase spectrum points is identical to that of the corresponding power spectrum points. It is shown that the BIFORE and discrete Fourier phase spectra have several analogous properties. A fast algorithm which yields the BIFORE power and phase spectra in approximately N log2 N arithmetic operations is also developed.
10 citations
TL;DR: In this paper, a linear iterative method for evaluating the Moore-Penrose generalized inverse of a matrix is described and conditions for optimizing its rate of convergence are given, where conditions for the convergence rate of the generalized inverse are given.
Abstract: A linear iterative method for evaluating the Moore-Penrose generalized inverse of a matrix is described and conditions for optimizing its rate of convergence are given
9 citations
TL;DR: An operational model which allows the complete formal definition of the full syntax and semantics of programming languages is described, both its syntactic and semantic parts are based on so-called linked-forest manipulation systems which allow the definition of mappings on forests.
Abstract: An operational model which allows the complete formal definition of the full syntax and, particularly, semantics of programming languages is described. Both its syntactic and semantic parts are based on so-called linked-forest manipulation systems which allow the definition of mappings on forests. The idea of “linking” is crucial for the given model, we represent not only abstract programs but also intermediate states of our system (abstract computer) by labelled forests with pointers.
8 citations
TL;DR: The characterization of this automaton and some corollaries stated here will allow it to be shown that systematic prefix codes are involved in the structure of any regular prefix code.
Abstract: Systematic prefix codes play an important role in coding theory, we relate them with the problem of the partition of a free (sub-) monoid into two free sub-monoids. We show too that among the dual codes of a systematic prefix code A there exists one and only one which appears in the automaton recognizing A *. The characterization of this automaton and some corollaries stated here will allow us to show in further note that systematic prefix codes are involved in the structure of any regular prefix code. Work done under CNR contract No. R-l7-02-417-0-A.
7 citations
TL;DR: In this paper, an online method to compute the spectra associated with the Fourier transform M of a data sequence is developed, where M and N are finite positive integers, and the method provides a simple means of generating time-frequency-amplitude plots of Fourier power and phase spectra.
Abstract: An on-line method to compute the spectra associated with the Fourier transform M of a data sequence is developed, whereM and N are finite positive integers. This method provides a simple means of generating time-frequency-amplitude plots of Fourier power and phase spectra. Such plots may be used to display Fourier spectra for pedagogical purposes, and in the general area of the classification of transient waveforms whose durations are unknown. An illustrative example is included.
6 citations
TL;DR: The equivalence of many generative schemes is shown and new results are obtained on their interrelationships, closure properties, compositions and the preservation of families of languages under such schemes.
Abstract: In this paper a number of formal schemes for recognizing or generating of translations(binary relations on words)are studied, most of them already being known. Known results are surveyed and new results are obtained on their interrelationships, closure properties, compositions and the preservation of families of languages under such schemes. For various recognizing schemes(transducers)the equivalent generative schemes(generalized grammars)are exhibited. Also, the equivalence of many generative schemes is shown.
TL;DR: In this article, a comparison between a certain version of invariant imbedding and the method of superposition, as represented by the Goodman-Lance method of complementary functions, with regard to their computational efficiency and effectiveness for linear two-point boundary-value problems is made.
Abstract: A comparison is made between a certain version of invariant imbedding and the method of superposition, as represented by the Goodman-Lance method of complementary functions, with regard to their computational efficiency and effectiveness for linear two-point boundary-value problems. The comparison is most complete for the class of problems termed normal. For such problems superposition appears to be preferable for problems with a sufficiently short underlying interval, on grounds of lesser effort, but the accuracy of super position degenerates more rapidly than that of invariant imbedding as the interval length increases, and consequently the latter method seems preferable for long problems. General areas of possible future investigation are identified.
TL;DR: The family of BDG languages with a particular yield operation was shown to be exactly the family of programmed languages in this article, which is the case for all of the languages in this paper.
Abstract: The family of BDG languages with a particular yield operation is shown to be exactly the family of programmed languages.
TL;DR: In this paper, a fourth order finite difference scheme for obtaining an approximate solution of second order linear differential equation lacking the first derivative, with mixed boundary conditions, is presented, and the convergence of the method is proved.
Abstract: A fourth order finite difference scheme for obtaining an approximate solution of second order linear differential equation lacking the first derivative, with mixed boundary conditions, is presented. The convergence of the method is proved. A numerical illustration is included to demonstrate the practical usefulness of our method.
TL;DR: In this article, a spectral representation for time series analysis is formulated on the basis of classical least-squares theory, and is extended for application to the prediction of a random sequence with a sequential updating of model coefficients based on pre-computed eigenvector components and current online data.
Abstract: A spectral representation for time series analysis is formulated on the basis of classical least-squares theory, and is extended for application to the prediction of a random sequence with a sequential updating of model coefficients based on pre-computed eigenvector components and current online data. The solution for updating the time series coefficients is shown to be directly analogous to the form of piecewise solution of the steady-state electrical network problem based on Kron's method of tearing and interconnection. The sensitivity of the spectral prediction algorithm based on the eigenvalue properties of the defining covariance data matrix is also developed.
TL;DR: The language allows a syntactic and semantic definition of the language being described, and is an extension of standard BNF, and applies it to describe a dialect of FORTRAN II.
Abstract: This paper describes a language-description language and applies it to describe a dialect of FORTRAN II. The language allows a syntactic and semantic definition of the language being described, and is an extension of standard BNF. The semantics is described by associating with each nonterminal in the syntactic description one or more state vector functions as semantic attributes in the sense of Knuth. Both synthesized and inherited attributes are allowed. Other attributes, such as length, value, environment, and the like, may also be used in a language description. The language-description language is given a partial definition in its own terms.
TL;DR: In this article, the Lax-Wendroff procedure is extended to the scalar case of a two-dimensional hyperbolic conservation law and explicit third and fourth order accuracy finite-difference operators are constructed for solving quasi-linear initial value problems.
Abstract: : In this paper the Lax-Wendroff procedure is extended to the scalar case of a two-dimensional hyperbolic conservation law. Explicit third and fourth order accuracy finite-difference operators are constructed for solving quasi-linear initial value problems. Stability conditions are obtained and are used in numerical computations. The computational results which are presented demonstrate that large amounts of computing time and memory space are saved without loss of accuracy. (Author)
TL;DR: This paper deals with a syntax-directed parsing scheme being used in a PL/I compiler for the CDC 6600, using a highly restricted grammar of the class LL(1) for efficiency, with an escape hatch for those cases excluded by the grammar.
Abstract: This paper deals with a syntax-directed parsing scheme being used in a PL/I compiler for the CDC 6600. It uses a highly restricted grammar of the class LL(1) for efficiency, with an escape hatch for those cases excluded by the grammar. These cases are handled by oracles that can make decisions without a full-scale syntactic analysis. The input to SYNDIPAR, the SYNtax Directed PARser, consists of syntax equations, semantic routines, and token class definitions; the output consists of a PARSE procedure in PL/I together with certain tables. The PARSE procedure works in conjunction with a lexical scanner, designed to allow look-ahead by oracles in a uniform fashion. The actual parsing process takes place through the interpretation of a program compiled by SYNDIPAR for a parsing machine. The instruction set of the parsing machine is described, and an example of the compilation of a syntax equation is given.
TL;DR: In this paper, a finite difference method for obtaining sixth order accurate approximation to the solution of the two-point linear boundary value problem is given, and the convergence of the method is proved.
Abstract: A finite difference method for obtaining sixth order accurate approximation to the solution of the two-point linear boundary value problem is given. The convergence of the method is proved. Numerical results for a typical problem are tabulated and in each case the observed error is compared with its theoretical estimate. The numerical results are compared with those obtained from an earlier method of the author and the method of Noumerov.
TL;DR: Algorithm to reduce the search time of linear pre-cedence functions used to compress the information of certain precedence matrices and preserve some of the error checking capability of the matrix.
Abstract: Linear precedence functions can be used to compress the information of certain precedence matrices. While saving space, the method applied to Wirth-Weber precedence matrices causes the detection of errors to be occasionally delayed. When shift-reduce decisions are based on a weak precedence grammar, however, it is often possible to find linear pre-cedence functions which preserve some of the error checking capability of the matrix. While the maximization of the amount of error checking is a large combinatorial problem, algorithms to reduce the search time can be given.
TL;DR: The related structures of two regular prefix codes generating languages recognized by isomorphic automata are given.
Abstract: We give here the related structures of two regular prefix codes generating languages recognized by isomorphic automata
TL;DR: A language for specifying lexical scans is described, which uses the model of a finite state automation with a limited back-up facility and is machine independent except for one statement which depends on the machine's character set.
Abstract: A language for specifying lexical scans is described.The language uses the model of a finite state automation with a limited back-up facility.It is efficiently implementable and is machine independent except for one statement which depends on the machine's character set.
TL;DR: A modification of Viswanathan's algorithm for the simultaneous extraction of polynomial roots is proposed in this paper, where the Fletcher-Powell adaptation of Davidson's algorithm is used instead of the method of steepest descent used by VISwanathan.
Abstract: A modification of Viswanathan's algorithm for the simultaneous extraction of polynomial roots is proposed. The Fletcher-Powell adaptation of Davidson's algorithm is used instead of the method of steepest descent used by Viswanathan. The modified algorithm is illustrated using the example treated by Viswanathan.
IBM1
TL;DR: The Goodman-Lance method of adjoints for solving two point boundary value problems of systems of non-linear ordinary differential equations is extended to handle the most general boundary conditions and specialized to several important subcases as discussed by the authors.
Abstract: The Goodman-Lance method of adjoints for solving two point boundary value problems of systems of non-linear ordinary differential equations is extended to handle the most general boundary conditions and specialized to several important subcases.
TL;DR: This paper presents the detailed development of a linear model for the computed solution to the linear system Ax = b; this model consists of an initial transcribing error plus a random part to model round-off.
Abstract: This paper presents the detailed development of a linear model for the computed solution to the linear system Ax = b; this model consists of an initial transcribing error plus a random part to model round-off. Discussed are general implications and techniques for the appli-cation of the model towards diminishing the effects of both.
TL;DR: This paper presents examples of a blending of two well-known formalisms, the ,λ-calculus and Markov normal algorithms, and illustrates the additional expressive power of the combined formalism.
Abstract: Most attempts to explain some aspect of computation formally have relied on a single formalism. This paper presents examples of a blending of two well-known formalisms, the ,λ-calculus and Markov normal algorithms, and illustrates the additional expressive power of the combined formalism.