Showing papers in "International Journal of Computer Mathematics in 1979"
TL;DR: A new factorisation method for the solution of a linear system is proposed that is similar to an LU type factorisation of the coefficient matrix A where the factors are interlocking matrix quadrants and can be applied on a single-instruction stream parallel machine.
Abstract: A new factorisation method for the solution of a linear system is proposed. The method is similar to an LU type factorisation of the coefficient matrix A where the factors are interlocking matrix quadrants and can be applied on a single-instruction stream parallel machine.
97 citations
TL;DR: In this paper, a one-parameter family of sixth-order methods for finding simple zeros of nonlinear functions is developed, each member of which requires three evaluations of the given function and only one evaluation of the derivative per step.
Abstract: A one-parameter family of sixth-order methods for finding simple zeros of nonlinear functions is developed Each member of the family requires three evaluations of the given function and only one evaluation of the derivative per step
78 citations
TL;DR: The existence of orderly analogues of graph generators proposed by Heap and Farrell is established as mentioned in this paper, and modifications to these algorithms supply practical methods enabling one to generate exhaustive lists of graphs and locally restricted graphs; moreover, the difficulty involved in ensuring that no duplications occur in the list is greatly reduced.
Abstract: The existence of orderly analogues of graph generators proposed by Heap and Farrell is established. The modifications to these algorithms supply practical methods enabling one to generate exhaustive lists of graphs and locally restricted graphs; moreover, the difficulty involved in ensuring that no duplications occur in the list is greatly reduced.
32 citations
TL;DR: This note first introduces the concept of “functions acceptable by two-dimensional finite automata” and then gives several functions unacceptable by three-dimensional infinite automata.
Abstract: In this note, we first introduce the concept of “functions acceptable by two-dimensional finite automata” and then give several functions unacceptable by two-dimensional finite automata.
20 citations
TL;DR: Various decidability problems of SF-languages, i.e. sets of sentential forms, of Chomsky grammars are studied and strongest possible undecidability and decidable results are looked for.
Abstract: Various decidability problems of SF-languages, i.e. sets of sentential forms, of Chomsky grammars are studied. Among the problems are the equivalence, ambiguity, equality to a regular set, and regularity of SF-languages, and the SF-ness of regular languages. All of these problems are undecidable for type 0 grammars, and many of them are decidable for minimal linear grammars. Strongest possible undecidability and decidability results are looked for.
12 citations
TL;DR: The following problems are shown to be decidable given an ETOL language L and two homomorphisms h 1 h 2 is the length (Parikh vector) of h 1(x) and h 2 h 2 (x) equal for each x in L? as mentioned in this paper.
Abstract: The following problems are shown to be decidable Given an ETOL language L and two homomorphisms h 1 h 2is the length (Parikh vector) of h 1(x) and h 2(x) equal for each x in L? If Lis over a binary alphabet then we can also test whether h 1(x)= h 2(x) for each x in L
9 citations
TL;DR: A hybrid version of the slant (ST) and Haar Transforms (HT) called slant-Haar transform (SHT) is developed and its utility and effectiveness are compared with other discrete transforms in applications such as feature selection, Wiener filtering and data compression.
Abstract: A hybrid version of the slant (ST) and Haar Transforms (HT) called slant-Haar transform (SHT) is developed. Its properties and fast algorithms are also developed. Based on some standard performance criteria its utility and effectiveness are compared with other discrete transforms in applications such as feature selection, Wiener filtering and data compression.
8 citations
TL;DR: The results obtained for a set of integrals with singularities at the endpoints using the Harris and Evans modified ten points Gauss formula are compared with those using Stenger's formula.
Abstract: The results obtained for a set of integrals with singularities at the endpoints using the Harris and Evans modified ten points Gauss formula are compared with those using Stenger's formula. While the Gaussian approach gives better results for a comparable number of points, the Stenger rule is easily applied with an arbitrary number of nodes and the comparison should be more favorable when more nodes are used.
7 citations
TL;DR: A stationary word of a OL system G=(X,P,w) is a word that generates itself after a positive number of direct derivations.
Abstract: A stationary word of a OL system G=(X,P,w) is a word that generates itself after a positive number of direct derivations. The stationary set of G is the set of stationary words of G and the stationary language of G is the set of the stationary words generated by w. The stationary set of G is a submonoid of X * containing the adult set of G. A language not containing the empty word is context-free if and only if it is the stationary language of a propagating system. Every TOL language is the image under a coding of the stationary language of a TOL system.
6 citations
TL;DR: In this paper, a recursive algorithm for the implicit derivation of the determinant of a symmetric sparse quindiagonal matrix derived from the finite difference discretisation of a self adjoint elliptic partial differential equation in a two-dimensional rectangular domain is developed in terms of its leading principal minors.
Abstract: A recursive algorithm for the implicit derivation of the determinant of a symmetric sparse quindiagonal matrix derived from the finite difference discretisation of a self adjoint elliptic partial differential equation in a two-dimensional rectangular domain is developed in terms of its leading principal minors. The algorithm is shown to yield a sequence of polynomials from which the eigenvalues can be obtained by use of the well-known bisection process. Modifications to the inverse iteration method to allow for sparsity of the matrix arrays yields the required eigenvectors.
5 citations
TL;DR: In this article, a method for calculating values of Bessel functions of the first kind Jv (z) is described, which requires only a knowledge of their zeros in order to evaluate a simple analytic formula.
Abstract: A method for calculating values of Bessel functions of the first kind Jv (z) is described, which requires only a knowledge of their zeros in order to evaluate a simple analytic formula. A simple error formula is derived and its behaviour as a function of z and v are described. Numerical examples of the error involved in approximating Jv (z) for and v=0,1 are given.
TL;DR: A factorization procedure in algorithmic form is derived yielding direct and iterative methods of solution of some interesting boundary value problems in physics and engineering.
Abstract: The numerical solution of partial differential equations in 3 dimensions by finite difference methods leads to the problem of solving large order sparse structured linear systems. In this paper, a factorization procedure in algorithmic form is derived yielding direct and iterative methods of solution of some interesting boundary value problems in physics and engineering.
TL;DR: In this article, a numerical method applied to the differential equation y′=λy can lead to a solution of the form, where z and w = λh satisfy an equation P(w, z) = 0.
Abstract: A numerical method applied to the differential equation y′=λy can lead to a solution of the form , where z and w = λh satisfy an equation P(w, z) = 0. In general P(w,z) is a polynomial in both w and z, of degree M in w and N in z. Existing multistep and Runge-Kuta methods correspond to the cases M = 1 and N = 1 respectively. New methods are fottd by taking MS≧2N≧2. The approach here is first to find a suitable polynomial P(w,z) with the desired stability properties, and then to find a process which leads to this polynomial. Third- and fourth-order A- and L-stable processes are given of the semi-explicit arid linearly implicit types.
TL;DR: It is shown that if the basic method for eliminating single productions from canonical LR parsers developed by Pager is applied to an SLR parser and the resulting parser is free of conflicts, then the resultingparser is a valid parser which accepts exactly the strings in the language.
Abstract: It is shown that if the basic method for eliminating single productions from canonical LR parsers developed by Pager is applied to an SLR parser and the resulting parser is free of conflicts, then the resulting parser is a valid parser which accepts exactly the strings in the language. However, if the elimination process is performed during the construction of an SLR parser, then the resulting parser may be invalid even if it were free of conflicts.
TL;DR: A method is presented that for each class of K-iteration grammars provides a class of acceptors for the corresponding class of languages, and it is shown that a simple (and natural) extension of a PDA2model yields aclass of acceptor for the class of recursively enumerable languages.
Abstract: The classes of languages accepted by (unrestricted) PAC machines and (unrestricted) PDA2machines are characterized. Several extentions of the PAC machine model are defined and in particular: (i) a method is presented that for each class of K-iteration grammars provides a class ofacceptors for the corresponding class of languages, and (ii) it is shown that a simple (and natural) extension of a PDA2model yields a class of acceptors forthe class of recursively enumerable languages.
TL;DR: In this paper, it was shown that for any bicolored-digraph-grammar system (with or without choice) there is an equivalent binary system in canonical form and that the generative capacity of these systems is not modified by considering initial vertices in the graph.
Abstract: We prove that for any bicolored-digraph-grammar system without choice there is an equivalent such system in canonical form. This provides an alternative solution (cf. [3]) to Problem 1 raised by D. Wood in [2]; the choice does not modify the generative capacity of these systems. Then it is shown that for any bicolored-digraph-grammar system (with or without choice) there is an equivalent binary system. Finally we shall prove that the generative capacity of these systems is not modified by considering initial vertices in the graph. This is true also for final vertices
TL;DR: A process of minimal degree is constructed using recursive processes and relative recursion for processes and the degree theory of processes is studied.
Abstract: A general definition of a process is given. Recursive processes and relative recursion for processes are defined and the degree theory of processes is studied. We construct a process of minimal degree
TL;DR: The notion of a KOL system, that is a deterministic tabled OL system where the use of the tables is regulated by the concentration of the letters in a word, is introduced and some decision problems are shown to be decidable for a special type of KOL languages.
Abstract: The notion of a KOL system, that is a deterministic tabled OL system where the use of the tables is regulated by the concentration of the letters in a word, is introduced. The relationship of KOL languages and KOL growth functions with languages and growth functions of other L systems is studied. The effect of the use of homomorphisms and nonterminals to the generative power is investigated. Some decision problems are shown to be decidable for a special type of KOL languages.
TL;DR: In this paper, an algorithm is introduced for finding zeros of polynomials with real as well as complex coefficients based on the geometrical and functional properties of poynomials.
Abstract: An algorithm is introduced for finding zeros of polynomials with real as well as complex coefficients. Based on the geometrical and functional properties of polynomials, the method can determine accurate distinct and repeated zeros of polynomials. The convergence of Newton's method plays an important role in this method. It has been found that the region of convergence by Newton's method is adequate. The important feature of this procedure is the obtaining of zeros of polynomials by combining Newton's method, synthetic division and functional properties of polynomials. The algorithm has been tested on many examples and numerical calculations have produced a greater degree of accuracy.
TL;DR: In this paper, an algorithm to compute the eigenvalues/functions of the Laplacian operator within a region with a sharp corner or line segment is given, based on the Dew and Scraton (1973) method.
Abstract: An algorithm to compute the eigenvalues/functions of the Laplacian operator within a region with a sharp corner or line segment is given. Point matching is used around the boundary and the algorithm is based on the Dew and Scraton (1973) method. It is shown that the numerical solution is an exact solution of a perturbed form of the problem and error estimates are obtained. A transformed problem, which eliminates the zero eigenvalue, is used for the Neumann problem.
TL;DR: A new class of grammars (precedence-regular Grammars) is obtained as a proper extension of the class of weak precedence grammARS, using Domolki's algorithm.
Abstract: A new class of grammars (precedence-regular grammars) is obtained as a proper extension of the class of weak precedence grammars. A parsing algorithm is described for this class of grammars, using Domolki's algorithm. Finally a criterion is obtained to decide whether a given context-free grammar belongs to this class.
TL;DR: It is shown that an arbitrary matrix form with only one nonterminal symbol does not generate the family of context-free languages if it contains a matrix with at least two productions.
Abstract: This paper deals with the concepts of a matrix form and strict interpretation. By a matrix form we mean a context-free matrix grammar. Via an interpretation mechanism it generates a family of structurally related grammars and these generate a family of languages. We study here the properties of matrix forms as generators for the families of regular, linear and context-free languages. It is for instance shown that an arbitrary matrix form with only one nonterminal symbol does not generate the family of context-free languages if it contains a matrix with at least two productions.
TL;DR: In this article, a mixed method using both the finite element technique and the finite difference method is developed for the solution of unsteady flow problems, which is based on choosing an interpolation function which is dependent only on the time domain.
Abstract: A mixed method using both the finite element technique and the finite difference method is developed for the solution of unsteady flow problems. The method is based on choosing an interpolation function which is dependent only on the time domain. The resulting local Galerkin finite element equations are obtained and assembled into a global form. The spatial derivatives of a variable at the nodes are replaced by a spatial operator (finite difference operator). The discretized nonlinear algebraic system is solved by an iterative scheme. The method is used to obtain the solution for the one-dimensional Burger's equation (model problem). The agreement of the results with other numerical and analytical solutions is quite good for cases in which the viscous effects are small (v≥0,1). The effects induced by changes in the step sizes are discussed. A quantitative comparison of the computing time is made of the related numerical techniques.
TL;DR: A new method for the numerical solution of non linear parabolic equations is presented, an extension of an existing algorithm for linear equations that appears to be both accurate and economical.
Abstract: A new method for the numerical solution of non linear parabolic equations is presented. The method is an extension of an existing algorithm for linear equations. Solutions are obtained in the form of a Chebyshev series, which is produced by approximating the partial differential equation by a set of ordinary differential equations over a small time interval. The method appears to be both accurate and economical.
TL;DR: A model is presented that concentrates on possible conditions that may exist in a system of n processes and k resource types with varying units of resources that is based on a graph in which each node represents a state of the entire system.
Abstract: Many models are present in the literature that have been used for investigating deadlock avoidance, prevention, and detection algorithms. In this paper, a model is presented that concentrates on possible conditions that may exist in a system of n processes and k resource types with varying units of resources. The model is based on a graph in which each node represents a state of the entire system. It can be shown that this set of nodes can be partitioned into three sets such that all nodes in the first set represent the condition that the corresponding system is guaranteed to be free of deadlock; the second set represents the condition that the system is deadlocked; the third set represents the condition that the system may or may not be in a state of deadlock, depending on how each given node has been reached from the initial node of the graph. The model has been exercised with various system configurations to obtain probabilistic estimates of deadlock existing in each node of the third sets, and these r...
TL;DR: This paper deals with certain characterizations of the sets of positive integers which when represented as strings on a finite alphabet, form tree adjunct languages, and the results carry over to the context free languages as well.
Abstract: This paper deals with certain characterizations of the sets of positive integers which when represented as strings on a finite alphabet, form tree adjunct languages, As the context free languages constitute a subfamily of tree adjunct languages, the results carry over to the former as well.
TL;DR: A recursive version of the Turing machine model is used to analyze the time and storage complexity of recursive algorithms and Hierarchy theorems are proven for time and for width of recursion.
Abstract: A recursive version of the Turing machine model is used to analyze the time and storage complexity of recursive algorithms. Hierarchy theorems are proven for time and for width of recursion (the amount of storage used at a level). A particular language is shown to be the “hardest” language to recognize without recursion. Previous results relating recursive and non-recursive time bounded computations are sharpened.
TL;DR: In the present note, a proof of the theorem expressing the fact that the push-down automata accept exactly the context-free languages is given.
Abstract: In the present note we give a proof of the theorem expressing the fact that the push-down automata accept exactly the context-free languages. The formulation of the proof (which follows the outline of the classical proof by Hopcroft and Ullman) aims at displaying some of the peculiarities of the situation. An example of the use of the constructive proof is given.