Showing papers in "Journal of Computational and Applied Mathematics in 1976"
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TL;DR: Interesting advantages of this program are the strong adaptivity of the algorithm combined with the use of a good basic integration rule and some comparative tests with other programs.
93 citations
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43 citations
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TL;DR: In this article, a family of cubature rules for approximating the double integral of f(u, v) over a triangle with vertices (u i, v i ) = 1, 2, 3 is presented.
30 citations
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TL;DR: In this article, a simple method for constructing quadrature rules for the numerical integration of an analytic function over a line segment in the complex plane is given, and an error analysis is used to show how rules preferable to the Birkhoff-Young rule are easily developed.
28 citations
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25 citations
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23 citations
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TL;DR: The results and conclusions of the study of 10 FORTRAN and ALGOL programs for solving non-linear equations with one unknown, without using derivatives, are given.
23 citations
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TL;DR: Two methods to compute Pade approximants are given based on the interpretation of the ϵ-algorithm of Wynn as the solution of a system of linear equations with an Hankel matrix recursively computed a sub-diagonal of the Pade table.
21 citations
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TL;DR: Some one step methods, based on nonpolynomial approximations, for solving ordinary differential equations are derived, and numerically tested, and a comparison is made with existing methods.
15 citations
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TL;DR: In this article, the authors considered the problem of finding the necessary and sufficient conditions to be fulfilled by the components of a hamiltonian operator to have an eigenvalue density with certain prescribed characteristics.
14 citations
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TL;DR: In this article, two determinants whose ratio is the Hughes Jones approximant to a power series in two variables are presented, which are generalizations of Jacobi's determinants for Pade approximants.
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TL;DR: In this article, the authors demonstrate a method of expanding Feynman amplitudes about a point in the upper half s-plane, and re-summing by the Pade method.
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TL;DR: In this paper, the theory of complex variables is used to develop exact closed-form solutions of the transcendental equation x coth x = α x 2 + 1, where the parameter α is considered to be real and the reported analysis yields analytical expressions, in terms of elementary quadratures, for the real solutions x, as they depend on prescribed values of α.
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TL;DR: In this article, a cubic spline approximation was used to produce finite difference representations of the homogeneous heat equation in one spatial variable, and the usual explicit and implicit formulae are particular cases of the formulations given here.
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TL;DR: In this paper, the best rational function approximation for Laplace transform inversion due to Longman is modified by the introduction of an appropriate "window" function, which enables one to approximate the inverse transform f(t) by a linear combination g n (t) of n exponential functions accurately.
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TL;DR: In this paper, a nonlinear mathematical model for the description of tidal flow propagation at the confluence of two tidal rivers is presented, which requires no additional approximations than what is usually accepted in the case of a single channel without branching.
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TL;DR: In this article, a matrix vector formalism is developed for systematizing the manipulation of sets of nonlinear algebraic equations, all manipulations are performed by multiplication with specially constructed transformation matrices.
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TL;DR: In this article, the authors consider the problem of which procedure is more efficient, i.e., which procedure produces the smallest error, when the number of operations needed to evaluate both sides of the above equations by means of the Pade approximations and polynomial noted are the same.
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TL;DR: In this article, it was shown that for any S 2n+1-point Gauss interpolation formula, r = [ n/2] + 1, r−1 of the nodes must lie within the interval [a, b], and the remaining node (which may or may not be in [a and b]) must be real.
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TL;DR: In this article, the polynomials A(n), B(n) are chosen so that S(1n) has coefficients of powers of n (and n−1) equal to those in a given divergent series T (1n).
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TL;DR: In this paper, the question of which type of terms do and do not falsify the shock speed is investigated and it is demonstrated that, when falsification occurs, it can be predicted, both qualitatively and quatitatively.
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TL;DR: In this paper, the optimal numerical approximation of bounded linear functionals by weighted sums in Hilbert spaces of functions defined in a domain B ⊂ C or B⊂ Rm, invariant in rotation or translation (e.g., circle, circular annulus, ball, spherical shell, strip of the complex plane) and equipped with inner product invariance in rotation and translation are considered.
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TL;DR: In this article, a two-component Borel algorithm with quadratic terms in the integrands involved was proposed as a summing technique for descending series in descending series, and the linear equations which arise have been triangulated, so that approximants to the original series are simple to set up and not as subject to roundoff error as other approaches.
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TL;DR: A derivation is given of the Levinson algorithm for solving systems with a symmetric positive definite Toeplitz matrix based on an orthogonalization technique.
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TL;DR: In this paper, important properties of the conjugate points are discussed and illustrated for the problem of optimizing the control of a direct-current electric motor, and they are shown to have significant implications for the optimization problems.
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TL;DR: In this paper, an iterative algorithm for the determination of the orthogonal P minimizing /vbPA - B /Vb F 2 is proposed and convergence is proved under natural assumptions.
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TL;DR: In this paper, a general and flexible analytic continuation method for power series is presented, which does not have the drawback of limiting processes and is potentially a strong competitor to the Pade approximant.