Showing papers in "International Journal of Computer Mathematics in 1985"
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TL;DR: In this article, the Alternating Group Explicit (AGE) method is applied to derive the solution of a 2-point boundary value problem and the analysis clearly shows the method to be analogous to the A.I.D. method.
Abstract: In this paper, the Alternating Group Explicit (AGE) method is developed and applied to derive the solution of a 2 point boundary value problem. The analysis clearly shows the method to be analogous to the A.D.I. method. The extension of the method to ultidimensional problems and techniques for improving the convergence rate and attaining higher order accuracy are also given.
171 citations
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TL;DR: The P-sequences which are integer sequences characterizing binary trees and generating lexicographically all the binary trees in -order are introduced and the L- sequences, also called natural order, are introduced.
Abstract: We introduce in this paper the P-sequences which are integer sequences characterizing binary trees and generating lexicographically all the binary trees in -order. We compute the rank of a P-sequence by a direct formula and not by an algorithm. Furthermore, we introduce the L-sequences which generate directly and lexicographically all the binary trees on A -order, also called natural order. Ranking and unranking algorithms are provided.
63 citations
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TL;DR: It is shown that computing the block LU decomposition of A is twice more efficient than computing the usual LU decompositon of A and the systolic solution of linear systems of matrix A is considered.
Abstract: After a brief discussion on systolic arrays for band matrix LU or QR decomposition, we introduce a new systolic array for the block 2x2 LU decompositon of a band matrix A. This array is an hexagonally connected systolic array whose efficiency is e = ½ although its hardware requirement is the same as the LU decomposition array of Kung and Leiserson [8]. In the last section we consider the systolic solution of linear systems of matrix A:: we show that computing the block LU decomposition of A is twice more efficient than computing the usual LU decomposition of A.
18 citations
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TL;DR: In this paper, a simple algorithm for globally minimizing a polynomial on a compact interval of the real line is proposed, which is based upon the idea of local approximation, is finitely convergent and reliable.
Abstract: A simple algorithm for globally minimizing a polynomial on a compact interval of the real line is proposed. The algorithm is based upon the idea of local polynomial approximation, is finitely convergent and reliable. Moreover, no derivatives of the polynomial are evaluated. Some examples of the numerical behavior of the algorithm are given.
17 citations
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TL;DR: In this paper, four time linearization techniques and two operator-splitting algorithms have been employed to study the propagation of a one-dimensional wave governed by a reaction-diffusion equation.
Abstract: Four time linearization techniques and two operator-splitting algorithms have been employed to study the propagation of a one-dimensional wave governed by a reaction-diffusion equation. Comparisons amongst the methods are shown in terms of the L 2-norm error and computed wave speeds. The calculations have been performed with different numerical grids in order to determine the effects of the temporal and spatial step sizes on the accuracy. It is shown that a time linearization procedure with a second-order accurate temporal approximation and a fourth-order accurate spatial discretization yields the most accurate results. The numerical calculations are compared with those reported in Parts 1 and 2. It is concluded that the most accurate time linearization method described in this paper offers a great promise for the computation of multi-dimensional reaction-diffusion equations.
14 citations
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TL;DR: This work presents a plane-sweep-based hidden-line-elimination algorithm for 2-dimensional projections of scenes consiting of arbitrary polyhedra, which requires, in the worst case, 0(n log n) space and 0((n + k) log2 n) time.
Abstract: Many practical algorithms for hidden-line and surface elimination in a 2-dimensional projection of a 3-dimensional scene have been proposed. However surprisingly little theoretical analysis of the algorithms has been carried out. Indeed no non-trivial lower bounds for the problem are known. We present a plane-sweep-based hidden-line-elimination algorithm for 2-dimensional projections of scenes consiting of arbitrary polyhedra. It requires, in the worst case0(n log n) space and 0((n + k) log2 n) time, where n is the number of edges in the 3-dimensional scene, and k is the number of edge intersections in the specific projection.
13 citations
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TL;DR: An initial approximation is proposed for use with Newton's method and sufficient conditions are obtained which guarantee convergence of Newton's Method with this initial appro-ximation and this initial approximation makes use only of the boundary data given in the two-point boundary value problem.
Abstract: For the numerical solution of non-linear two-point boundary value problems: the well-known Numerov's method leads to a non-linear system for the approximate solution. We consider here application of Newton's method for the solution of the resulting non-linear system. In this note we propose an initial approximation for use with Newton's method and obtain sufficient conditions which guarantee convergence of Newton's method with this initial appro-ximation and for all interestingly, this initial approximation makes use only of the boundary data given in the two-point boundary value problem.
13 citations
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TL;DR: The bijective mapping between the set of combinations and theSet of corresponding binary codewords is shown to be isotone, in lexicographic order, and a recursive algorithm for enumerating all combinations in lexICographic order is presented.
Abstract: A simple way of representing combinations as binary strings is discussed. The bijective mapping between the set of combinations and the set of corresponding binary codewords is shown to be isotone, in lexicographic order. A recursive algorithm for enumerating all combinations in lexicographic order is presented. Simple ranking and unranking algorithms for coding and decoding position indices of combinations in a lexicographic listing are also described.
11 citations
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TL;DR: Explicit mappings from the first n2p base n Gray code integers into the ordered vertices of the pth Peano polygon and vice versa are derived and the result is generalised to r-dimensional Peano polygons.
Abstract: Explicit mappings from the first n2p base n Gray code integers into the ordered vertices of the pth Peano polygon and vice versa are derived The result is generalised to r-dimensional Peano polygons Algorithms to achieve the transformations directly are discussed
9 citations
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TL;DR: The purpose of this paper is to found a fundamental theory of the parallel algorithms for solving P.D.E.'s on multiprocessors and the convergence of the algorithms are proved.
Abstract: The purpose of this paper is to found a fundamental theory of the parallel algorithms for solving P.D.E.'s on multiprocessors. The asynchronous parallel algorithm S-COR are defined. And the convergence of the algorithms are proved.
9 citations
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TL;DR: In this article, the propagation of a unidimensionnelle regie par une equation de reaction diffusion a l'aide de schemas numeriques is studied. Analyse comparative de la precision
Abstract: Etude de la propagation d'une onde unidimensionnelle regie par une equation de reaction diffusion a l'aide de schemas numeriques. Analyse comparative de la precision
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TL;DR: This paper presents the extreme performance of the promising Q.A.D. algorithm, for scheduling independent jobs under few pre-set ordering rules on the examined model, when the mean-flow time is the performance criterion and an algorithm is introduced that produces schedules with minimum mean- flow time.
Abstract: This paper presents the extreme performance of the promising Q.A.D. algorithm, for scheduling independent jobs under few pre-set ordering rules on the examined model, when the mean-flow time is the performance criterion. Further, an algorithm, based on the idea of Q.A.D., with complexity 0(n 2) is introduced that produces schedules with minimum mean-flow time.
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TL;DR: In this paper, a family of one-step multiderivative predictor-corrector methods were tested on a linear system where the matrix of coefficients has constant complex eigenvalues and on a stiff nonlinear system arising in reactor kinetics.
Abstract: Stability regions are plotted for certain members of a family of one-step multiderivative predictor-corrector methods developed by the authors in an earlier paper. The methods discussed are tested on a linear system where the matrix of coefficients has constant complex eigenvalues and on a stiff non-linear system arising in reactor kinetics.
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TL;DR: In this paper, the equivalence problem for deterministic two-way finite-state automata augmented by a bounded-reversal counter was shown to be decidable in general.
Abstract: Consider the emptiness problem for deterministic two-way finite-state automata that are augmented by a bounded-reversal counter and the equivalence problem for deterministic two-way finite-state transducers. The first problem was posed by Ibarra while the second problem restricted to the case that accepting configurations are also halting configurations was posed by Ehrich and Yau. Recently the first problem restricted to devices that accept only bounded languages as well as the restricted version of the second problem have been shown decidable. Here these two problems are shown decidable also in their general form.
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TL;DR: In this article, a nonlinear singular Volterra integral equation was derived to describe the temperature distribution of the surface of a projectile moving through a laminar boundary layer at high Mach numbers.
Abstract: Lighthill has derived a nonlinear singular Volterra integral equation to describe the temperature distribution of the surface of a projectile moving through a laminar boundary layer at high Mach numbers. This paper presents high order product integration methods for its numerical solution and analyses their convergence. Numerical results are given.
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TL;DR: It is shown that the parallel arithmetic computational complexities of the Cholesky's and QR factorization of a matrix are upper bounded by 0(log2 n) steps and a new parallel method for QR factorized of a symmetric positive definite tridiagonal matrix is proposed.
Abstract: In this paper, it is shown that the parallel arithmetic computational complexities of the Cholesky's and QR factorization of a matrix are upper bounded by 0(log2 n) steps Also, a new parallel method for QR factorization of a symmetric positive definite tridiagonal matrix is proposed This method requires only 0(logn) steps using 0(n) processors
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TL;DR: It is proved here that there are inner contextual grammars generating matrix languages of infinite index and each regular-conditional contextual grammar generates a context-free language.
Abstract: The paper deals with four open problems in the monograph [8], namely it is proved here that: (i) there are inner contextual grammars generating matrix languages ofinfinite index (a half of problem P3 in [8]), (ii) the inner contextual grammars with bounded choice can generate non-context-free languages (PI8 in [8]), (iii) each regular-conditional contextual grammar generates a context-free language (P13 in [8]) and (iv) the relations between contextual languages and L-families (P4 in [8] are investigated
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TL;DR: Two constructions of generalized Grammars are investigated and families of languages are studied for which these constructions provide grammars.
Abstract: Two constructions of generalized grammars are investigated and families of languages are studied for which these constructions provide grammars. One of these families coincides with the family of linear languages, another includes the family of linear deterministic languages and the family of contextual languages.
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TL;DR: For a rectilinear art gallery with nwalls at most [n/4] guards are needed to keep the entire art gallery under observation, the authors proved that n/4 guards are sufficient.
Abstract: The Rectilinear Art Gallery Theorem states that for a rectilinear art gallery with nwalls at most [n/4] guards are needed to keep the entire art gallery under observation. There have been two proofs of this result. The first proof depends on the quadrilateralization of the art gallery and is quite complicated. The second proof is direct, yet it depends on a graph-theoretic argument at one crucial point. Our proof, on the other hand, is direct, completely geometrical, and at the same time, simple.
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TL;DR: In this article, a symmetric rule for the approximate numerical integration of is given and criteria for optimising the parameters in that rule are chosen based on the parameters of the integration rule.
Abstract: Given a symmetric rule for the approximate numerical integration of we choose criteria for optimising the parameters in that rule. The method is extended to find integration rules in higher dimensions.
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TL;DR: In this article, it is shown that it is possible to develop nonequidistant predictor-corrector formulae with minimum error bounds for solving systems of differential equations such that the tedious difficulties which arise in practical applications can be overcome.
Abstract: This paper shows that it is possible to develop nonequidistant predictor-corrector formulae with minimum error bounds for solving systems of differential equations such that the tedious difficulties which arise in practical applications can be overcome. General predictor-corrector formulae with variable steps are constructed. Explicit third order- and fourth order-two points formulae are derived. Also fourth order-three points formulae are represented. Two theorems are given. A flow chart for general nonequidistant predictor-corrector methods using automatic control for the step length is compactly represented for solving systems of differential equations. These methods are recommended to be used widely in practice because of many advantages.
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TL;DR: This paper addresses the question of hardware implementation and presents several distinctly different supporting archi- tectures and both designs are analyzed and compared in terms of their speed-complexity tradeoffs.
Abstract: Fast and efficient implementation of a residue number to integer converters will be required to design fast residue number systems. This paper addresses the question of hardware implementation and presents several distinctly different supporting archi- tectures. Both designs are analyzed and compared in terms of their speed-complexity tradeoffs.
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TL;DR: The grammatical families of all languages generated by simple contextual grammars which are obtained by (strict) interpretations of a simple contextual grammar are investigated in this paper, and their hierarchies and their closure properties with respect to the AFL-operations are studied.
Abstract: The grammatical families of all languages generated by simple contextual grammars which are obtained by (strict) interpretations of a simple contextual grammar are investigated. Their hierarchies and their closure properties with respect to the AFL-operations are studied.
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TL;DR: It is shown, for example, that matrix multiplication is independent of any of the following problems: computing the transitive closure of a graph, the rank of a matrix, a set of independent rows and columns in a Matrix, a maximum bipartite matching, etc.
Abstract: We give a formal definition of a property which informally says that problem B is independent of problem A if the existence of an “oracle” which solves problem A at zero cost does not help to reduce the cost of any algorithm which solves problem B. We then show, for example, that matrix multiplication is independent of any of the following problems: computing the transitive closure of a graph, the rank of a matrix, a set of independent rows and columns in a matrix, a maximum bipartite matching, etc.
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TL;DR: A syntactically simple language is proposed that is exactly those which are polynomially computable by Turing Machines, thus enabling to define the problem as an equivalence problem of two languages.
Abstract: A syntactically simple language is proposed. The functions computable by this language are exactly those which are polynomially computable by Turing Machines. A similar nondeterministic language is also shown, thus enabling to define the problem as an equivalence problem of two languages.
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TL;DR: In this article, a modification of a Steffensen-type procedure is used to find a simple root of an equation, which produces two sequences of iterates, each of which converge to the root from opposite sides.
Abstract: In this paper a modification of a Steffensen-type procedure is used to find a simple root of an equation. The modified algorithm produces two sequences of iterates, each of which converge to the root from opposite sides. The method is illustrated using two numerical examples.
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TL;DR: In this article, a direct approach for single and multiple fault test set generation on any number of lines of a logical circuit has been described, for which only some visual inspections are needed rather than going through tedious steps of algebraic manipulations.
Abstract: A direct approach for single and multiple fault test set generation on any number of lines of a logical circuit has been described in this paper. The present paper simplifies the results of Ku and Masson [2] for which only some visual inspections are needed rather than going through tedious steps of algebraic manipulations. This method is thus easily applicable to arbitrarily large combinational circuits, whether it is fan-out free or with fan-out nodes.
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TL;DR: Syntactic properties of this language REFAL, one of the languages created for symbolic manipulation, are formally investigated.
Abstract: A programming language REFAL is one of the languages created for symbolic manipulation. It is implemented on various computers. Syntactic properties of this language are formally investigated in this paper.
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TL;DR: In this paper, a factorisation procedure for banded symmetric matrices which occur repeatedly in the solution of ordinary/partial differential equations under periodic boundary conditions is described, and the numerical solution to the derived special linear systems can then be obtained efficiently by a sequence of simple forward and back substitution processes.
Abstract: A factorisation procedure is described for certain banded symmetric matrices which occur repeatedly in the solution of ordinary/partial differential equations under periodic boundary conditions. The numerical solution to the derived special linear systems can then be obtained efficiently by a sequence of simple forward and back substitution processes.
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TL;DR: In this article, it was shown that there exists a recursive oracle A⊆{0, 1} such that some set in has no infinite subset in where is accepted by a X non-deterministic polynomial time bounded Turing machine with oracle B⊈{0, 1} making at most n non-independently determinable moves on any input of length n.
Abstract: We prove that for any k≧l there exists a recursive oracle A⊆{0,1}∗ such that some set in has no infinite subset in where is accepted by a X nondeterministic polynomial time bounded Turing machine with oracle A⊆{0,1}∗ making at most ni nondeterministic moves on any input of length n}.