Showing papers in "International Journal of Computer Mathematics in 1980"
TL;DR: In this paper, a one parameter family of one-point iteration formulae for solution of a single variable equation is presented, which includes the Halley's, Chebyshev's and Cauchy's formulas.
Abstract: In this paper a one parameter family of one-point iteration formulae for solution of a single variable equation is presented. The formulae are derived on the basis of one-point approximation by the four parameter function . The family includes the Halley's, Chebyshev's and Cauchy's formulae, and, as a limiting case, Newton's formula. All formulae of the family are cubically convergent to simple roots (except Newton's which is quadratically convergent).
34 citations
TL;DR: A new factorisation method suitable for the solution of linear systems and determinant evaluation is proposed based on a modification of a factorisation recently proposed by Evans and Hatzopoulos of the matrix in which interlocking matrix quadrant factors are considered in lieu of the (standard) well-known LU triangular factors.
Abstract: A new factorisation method suitable for the solution of linear systems and determinant evaluation is proposed. The method is based on a modification of a factorisation recentlyproposed by Evans and Hatzopoulos [1] of the matrix in which interlocking matrix quadrant factors are considered in lieu of the (standard) well-known LU triangular factors. The method can be considered of Choleski type for positive definite real symmetric matrices. The proposed method is suitable for use on a parallel machine of S.I.M.D. type.
29 citations
TL;DR: In this article, it was shown that for each recursively enumerable language there exists an erasing homomorphism h 0 and homomorphisms h 1, h 2 such that L = h 0(e(h 1,h 2)) where L is the set of minimal words on which h 1 and h 2 agree.
Abstract: Recently, it has been shown that for each recursively enumerable language there exists an erasing homomorphism h 0 and homomorphisms h 1,h 2 such that L= h 0(e(h 1,h 2)) where (e(h 1,h 2)) is the set of minimal words on which h 1 and h 2 agree. Here we show that by restrictions on the erasing h 0 we obtain most time-complexity language classes, and by restrictions on the pair (h 1 h 2) we characterize all space complexity language classes.
11 citations
TL;DR: In this paper, the problem of interpolating a function of several variables given only values at a finite number of points can be solved by modeling the function as a stationary stochastic process, and estimating the value at any unknown point from the known values by multiple regression, given some parameters of the process.
Abstract: The problem of interpolating a function of several variables given only values at a finite number of points can be tackled by modelling the function as a stationary stochastic process, and estimating the value at any unknown point from the known values by multiple regression, given some parameters of the stochastic process. One application of this approach is in producing contour maps from scattered data points in two dimensions.
11 citations
TL;DR: In this article, a parallel shooting method is proposed for the solution of nonlinear multipoint boundary value problems, which extends the usual quasilinearization method and a previous shooting method developed for such problems.
Abstract: A type of parallel shooting method is proposed for the solution of nonlinear multipoint boundary value problems. It extends the usual quasilinearization method and a previous shooting method developed for such problems, and reduces to usual multiple shooting techniques for two point boundary value problems. The effectiveness of the method for stiff problems is illustrated by an application to the problem of finding periodic solutions of a restricted three body problem with given Jacobian constant and unknown period.
8 citations
TL;DR: This general approach establishes a mathematical treatment of LR(k) parsing which does not rely on the actual construction of an LR( k) parser, and allows a decisive comparison of properties of different LR(K) parsers, as well as those optimized by the so-called default reductions.
Abstract: The paper is the first in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. An LR(k) parser of a context-free grammar is treated as a formal system where the derivations are reversals of rightmost derivations in the grammar. Deriving in the system is possible if and only if a corresponding reduction by the conventional LR(k) parser may occur. This general approach establishes a mathematical treatment of LR(k) parsing which does not rely on the actual construction of an LR(k) parser. For example, the approach allows a decisive comparison of properties of different LR(k) parsers, such as canonical LR(k), LALR(k) and SLR(k) parsers, as well as those optimized by the so-called default reductions.
7 citations
TL;DR: In this paper, the problem of determining a heuristic which maintains a doubly linked list in approximately optimal order with respect to mean search time is considered, and it is shown that in one particular case no such heuristic can be found, while in many other situations heuristics for similarly maintaining sequential lists should be used.
Abstract: The problem of determining a heuristic which maintains a doubly linked list in approximately optimal order with respect to mean search time is considered. Within a general framework of simple assumptions it is shown that in one particular case no such heuristic can be found, while in many other situations heuristics for similarly maintaining sequential lists should be used. In the remaining circumstances a heuristic known as move to end is shown to reduce search time, on average, to at most twice the minimum value determined by an optimal ordering of the list.
6 citations
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TL;DR: This paper considers an analogous extension of the LL(k) grammars called the LL-regular Grammars, an extension ofThe LR(k), and the relation of this class of grammARS to other classes of gramMars will be shown.
Abstract: Culik II and Cogen introduced the class of LR-regular grammars, an extension of the LR(k) grammars. In this paper we consider an analogous extension of the LL(k) grammars called the LL-regular grammars. The relation of this class of grammars to other classes of grammars will be shown. Any LL-regular grammar is an LR-regular grammar. Properties of LL(k) grammars can be generalized to properties of LL-regular grammars.
6 citations
TL;DR: In this article, the authors modify the approach of de Boor to cautious Romberg extrapolation by making a comparison between the results obtained from the trapezoidal and Simpson rules, which has the advantage that it gives some guidance regarding the estimation of the dominant terms involved.
Abstract: An automatic quadrature routine was presented by de Boor which was based on the use of the trapezoidal rule with “cautious Romberg extrapolation”. It is the object of this paper to modify the approach of de Boor to cautious Romberg extrapolation by making a comparison between the results obtained from the trapezoidal and Simpson rules. This has the advantage that it gives some guidance regarding the estimation of the dominant terms involved, requires no additional function evaluations, and only minor changes in de Boor's program CADRE are necessary to effect the proposed modifications. Special account is taken of integrands with end-point singularities and the possibilities of logarithmic terms being involved in the extrapolation. Further, indications are given of where automatic Romberg extrapolation can fail.
5 citations
TL;DR: In this article, a boundary integral equation for the numerical solution of a class of elliptic boundary value problems for a strip is derived, which is particularly useful for the solution of an important class of problems governed by Laplace's equation and also for relevant problems in anisotropic thermostatics and elastostatics.
Abstract: A boundary integral equation for the numerical solution of a class of elliptic boundary value problems for a strip is derived. The equation should be particularly useful for the solution of an important class of problems governed by Laplace's equation and also for the solution of relevant problems in anisotropic thermostatics and elastostatics
5 citations
TL;DR: A new class of syntax errors is introduced, called (k)-local parser defined errors, which suit better than the conventional minimum distance errors for characterization of error detection and recovery in LR(k) parsing.
Abstract: The paper is the third in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. A new class of syntax errors is introduced, called (k)-local parser defined errors, which suit better than the conventional minimum distance errors for characterization of error detection and recovery in LR(k) parsing. The question whether a given string has n k-local parser defined errors for some integer n is shown to be decidable. Using the formalization of LR(k) parsing and error recovery presented in the first and the second paper in the series it is shown that the canonical LR(k) parser of an LR(k) grammar always has an error recovering extension which is able to produce a correction for any terminal string containing only (k)-local parser defined errors.
TL;DR: In this article, a convergence theorem for numerical methods applied to the plate deflection boundary value problem was obtained. But it was only for the case where an approximation of O(hm ) was used at interior points and at least O(m-2 ) at boundary points, provided certain conditions were satisfied.
Abstract: A convergence theorem is obtained for numerical methods applied to the plate deflection boundary value problem. It is shown that if an approximation of O(hm ) is used at interior points and at least O(hm-2 )is used at boundary points then the results are O(hm-4 ) provided certain conditions are satisfied. A sixth order method is described in detail.
TL;DR: The treatment is based on the formalization of LR(k) parsing presented in the first paper in the series and it covers practically all error recovery methods designed for LR( k) parsing.
Abstract: The paper is the second in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. Error recovery in LR(k) parsing of a context-free grammar is formalized by extending an LR(k) parser of the grammar such that it accepts all strings over the terminal vocabulary. The parse produced by this extension for a terminal string is a right parse if the string is in the language. In the case of a string not in the language the parse produced by the extension contains so-called error productions which represent the error recovery actions performed by the extension. The treatment is based on the formalization of LR(k) parsing presented in the first paper in the series and it covers practically all error recovery methods designed for LR(k) parsing.
TL;DR: Two algorithms are presented and analyzed, which compute the distance between any pair of leaves of a complete tree, running in time O(log2 distance) on a uniform-cost RAM.
Abstract: Two algorithms are presented and analyzed, which compute the distance between any pair of leaves of a complete tree. The first algorithm is quite efficient, running in time O(log2 distance) on a uniform-cost RAM. The second algorithm is somewhat less efficient, though it too runs on a uniform-cost RAM in time O(log2 distance); it is presented mainly because its validity depends on an interesting numerological descriptor of complete trees.
TL;DR: It is proved that the minimal trees of the class of 2–3 brother trees and of theclass of strongly dense ternary trees have the same number of leaves.
Abstract: Dense multiway trees have been introduced recently. The question arises whether they can be compared to classes of balanced trees which are already known. This is the case for dense ternary trees and 2–3 brother trees. We prove that the minimal trees of the class of 2–3 brother trees and of the class of strongly dense ternary trees have the same number of leaves. We also correct an error in the original derivation of the number of keys in a minimal 2–3 brother tree.
TL;DR: A complete algorithm for computing acceptable assignments for the live variable problem in global program optimization is given which is a modification of an earlier algorithm due to Graham and Wegman which has been analysed on some self-replicating families of reducible flow graphs.
Abstract: A complete algorithm for computing acceptable assignments for the live variable problem in global program optimization is given which is a modification of an earlier algorithm due to Graham and Wegman. The complexity of the algorithm has been analysed on some self-replicating families of reducible flow graphs. It has been observed that there exists class of graphs for which algorithms of 0(nlog n) require more bit vector operations than algorithms of 0(n 2). A characterization of the flow graphs for which the procedure of Graham and Wegman is applicable for backward data flow propagation problems is also presented
TL;DR: In this paper, a new class of C 2 piecewise quintic interpolatory polynomials is defined, which contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline.
Abstract: A new class of C 2 piecewise quintic interpolatory polynomials is defined. It is shown that this new class contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline.
TL;DR: The non-procedural programming language Lucid is described formally using a model based on linked forest manipulation systems which is essentially non-deterministic and involves parallelism.
Abstract: The non-procedural programming language Lucid is described formally using a model based on linked forest manipulation systems. In this model the semantics is defined com-putationally by an abstract interpreter which is essentially non-deterministic and involves parallelism. This computational semantics is proven to be totally correct with respect to the denotational semantics of Lucid.
TL;DR: In this article, a fast quadrature formula using a logarithmically varying grid is investigated for a simplified model which crudely represents the eigensolutions obtained in the stability analysis of the flat plate turbulent boundary layer using the "variation-iteration" method and the Green's functions.
Abstract: A fast quadrature formula using a logarithmically varying grid is investigated. The accuracy of the formula is studied for a simplified model which crudely represents the eigensolutions obtained in the stability analysis of the flat plate turbulent boundary layer using the “variation-iteration” method and the Green's functions. This formula helps reduce the number of calls to evaluate the function being integrated without significant loss in accuracy. Application of this method to the original turbulence problem results in significant savings in machine time.
TL;DR: In this article, a method for computing the numerical solution to quasi-linear parabolic p.d.s using a Chebyshev method with mixed boundary conditions is presented. But this method is not suitable for the case of quadratic pd.
Abstract: Dew [1] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this note is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described.
TL;DR: A “negative parallel” version of Penttonen's normal form is found and the effect of forbidding context symbols to be within a certain distance from the symbol to be rewritten is limited.
Abstract: A random context production has a permitting and forbidding context. A symbol can be rewritten using such a production if all the permitting context symbols and no forbidding context symbol appear in the sentential string. In this paper we limit the effect of forbidding context symbols to be within a certain distance from the symbol to be rewritten. Outside this distance the forbidding context symbols do not influence the rewriting of a symbol. This restriction strictly increases the generating power of the rewriting system. A further result of this paper is a “negative parallel” version of Penttonen's normal form.
TL;DR: In this paper, a factorisation method is described for fast numerical solution of certain quindiagonal symmetric linear systems of special form which occur repeatedly in the solution of many initial and boundary-value problems containing fourth-order parabolic and elliptic partial differential equations under periodic or specified boundary conditions.
Abstract: A factorisation method is described for the fast numerical solution of certain quindiagonal symmetric linear systems of special form which occur repeatedly in the solution of many initial and boundary-value problems containing fourth-order parabolic and elliptic partial differential equations under periodic or specified boundary conditions. In this paper, we show that such special linear systems can be solved efficiently by an algorithm derived from the factorisation of the coefficient matrix into two easily inverted matrices.
TL;DR: This paper shall develop a means of locating parallelism in programs written in Algol-type languages by using an extension of a notation developed by Bernstein (1966).
Abstract: Over the past few years a number of methods have been formulated and implemented by which a programmer may explicitly indicate where parts of his program may be executed on different processors at the same time (Anderson, 1965). This, although useful in some circumstances, leaves the onus on the programmer to detect and express all possible parallelism in his program, as well as necessitating the rewriting of existing serial programs. These problems could be avoided if it were possible to automatically examine programs and indicate parallel relationships between parts of code. In this paper we shall develop a means of locating parallelism in programs written in Algol-type languages by using an extension of a notation developed by Bernstein (1966).
TL;DR: An algorithm for optimum realization of n × n distance matrix by a weighted digraph is presented and it is shown that the optimum realization is unique.
Abstract: In this paper we present an algorithm for optimum realization of n × n distance matrix by a weighted digraph. The method has two major steps. In the first step the index pairs of the nonzero finite elements of the given matrix are partitioned such that the elements corresponding to each class have the same value. The second step involves a systematic graph construction process that uses the information from the first step and an algorithm for computing a distance matrix for a digraph. We have proved the correctness of our algorithm and shown that the optimum realization is unique. An example is presented for illustrating the algorithm.
TL;DR: In this paper, the integrand function obtained when is reduced to an integral over t by using the transformation t=τ(x,y) is considered and an adaptive procedure is derived.
Abstract: Methods are discussed for calculating Q(t) which is the integrand function obtained when is reduced to an integral over t by using the transformation t=τ(x,y). The variations in τ(x,y) are considered and an adaptive procedure is derived. This differs from he standard quadrature problem in which the properties of f(x,y) dictate the adaptive procedures to be used. The one dimensional case is examined in detail.
TL;DR: In this paper, a formal model embedding the basic concepts of state-space problem solving is presented, and necessary and sufficient conditions for the existence of solutions of a problem are proved.
Abstract: This paper is devoted to present some algebraic properties of the state-space approach to problem solving. A formal model embedding the basic concepts of state-space problem solving is first presented. Necessary and sufficient conditions for the existence of solutions of a problem are proved. The new concept of resolvent set is then introduced and its mathematical characterization is presented. It is argued that the formal theory developed can support the development of new search techniques and complexity estimate methods.
TL;DR: Information theory is used for estimating the storage space needed for storing an (n×n)-table and the results are useful when comparing some compression techniques of files.
Abstract: Information theory is used for estimating the storage space needed for storing an (n×n)-table. Several different types of tables are considered. The results are useful when comparing some compression techniques of files