Showing papers in "Journal of Computational and Applied Mathematics in 1975"

TL;DR: An algorithm for fitting a smoothing spline function to a set of experimental or tabulated data is presented and the obtained spline approximation can be used for differentiation and integration of the given discrete function.

TL;DR: In this article, the Hermite polynomials of several variables are defined by a generalization of the Rodrigues formula for ordinary Hermite polynomials, and several properties are derived, including the differential equation satisfied by the polynoms and their explicit expression.

TL;DR: In this article, a nonadaptive automatic integration scheme using Clenshaw-Curtis quadrature is presented, and extensions are made to calculate Cauchy principal values and integrals having algebraic and logarithmic end point singularities.

TL;DR: In this article, a new cubic iteration method for determining simultaneously all the zeros of a polynomial (assumed distinct) starting with "reasonably close" initial approximations (also assumed distinct) is presented.

TL;DR: An adaptive quadrature method for the automatic computation of integrals with strongly oscillating integrand with a protection against the influence of round-off errors is presented.

TL;DR: The techniques used in this survey give some new ideas concerning the structure of the Pade table and the different ways to compute the elements of the table.

TL;DR: In this article, an orthogonalization procedure for a sequence of vectors having the special feature that consecutive vectors are related by a unitary operator is given for the least squares solution of linear equations with a cyclic rectangular coefficient matrix.

TL;DR: In this article, a semi-discrete Galerkin approximation of a parabolic mixed boundary-initial value problem is presented, and the solution of the resulting system of ordinary differential equations by implicit Runge-Kutta formulae for arbitrarily high order of accuracy is discussed.

TL;DR: In this article, a direct generalization of a convergence acceleration algorithm due to the author to infinite integrals is presented, and used to obtain an efficient method for numerical inversion of the Laplace transform.

TL;DR: In this article, the application of a method of least squares Laplace transform inversion due to the author is discussed, and examples are given, which also serve to give us best trigonometric and exponential function approximations to some known functions.

TL;DR: In this paper, a numerical method for constructing 25-point and 26-point cubature formulas with degree of exactness 11 is given for two-dimensional regions and weight functions which are both symmetric in each variable.

TL;DR: In this paper, a matrix vector formalism is developed for systematizing the manipulation of sets of non-linear algebraic equations, all manipulations are performed by multiplication with specially constructed transformation matrices.

TL;DR: Some convergence properties of these non-linear techniques, mainly based on the use of Pade approximation and rational interpolation, given for computing the value of a definite integral are proved.

TL;DR: A recursive method is given for the computation of the coefficients in the Chebyshev-Pade table, a table, recently defined by Clenshaw and Lord, which is analogous to the Pade table for power series.

TL;DR: A new algorithm for clique-detection in a graph rests on the so-called “decomposition of a graph into a chain of subgraphs” and on the corresponding “quasi-blockdiagonalisation” of the adjacency matrix.

TL;DR: A relaxed SOR-method is proposed; bounds for the spectral radius of the iteration operator are derived and the values of the corresponding iteration parameters can be directly calculated from the norm of the given matrix.

TL;DR: In this article, it is shown how integral transforms can be powerful computational tools even in quantum mechanics, a field where they are not usually applied, and how integral transform can be used in quantum computing.

TL;DR: In this paper, the expansion of a real square-integrable function in a Legendre series is considered and the existence of best approximations from different sets of exponential functions and their mean convergence to the function in question are proved.

TL;DR: A newly developed FORTRAN IV Program FUNMIN-2, which is based on the original DFP-method incorporating a few computationally significant modifications has been compared with the FORTRan version of the ALGOL procedure FLEPOMIN (1966).

TL;DR: In this article, a new algorithm for treating numerically a pentadiagonal matrix is given, and the stability of the solution of some difference equations is examined, as an application the evaluation of the eigenvalues is performed.

TL;DR: The stability of the algorithm is examined, some examples are given of experimental convergence rates for the interpolation of elementary analytical functions, and a listing of the two FORTRAN subroutines INSPL5 and SPLIN5 which form the algorithm.

TL;DR: A comparison for a range of linear equation problems Ax = b between LINSYS, IBMSSP and IMSL is made.

TL;DR: In this paper, the Hermite interpolation method is described in a simplified form and the formulae are derived, where the derivatives of the interpolating polynomials are not known.

TL;DR: An attempt is made to introduce the non-expert reader to the many aspects of a relatively new and varied field which seems to be at the same time analysis, algebra and computer science.

TL;DR: In this paper, an extension or modification of the output of least-squares computer subroutines is proposed in order to enable the researcher, who is confronted with an unreasonable parameter estimate, to investigate the effect of changing this value on the other parameter estimates and the estimated residual variance by simple hand computation.

TL;DR: In this paper, a regular perturbation problem for a time optimal control problem in which the optimal controller is bang-bang was formulated, and a technique based on the idea of introducing a nonlinear change of variables which freezes the switch times and the terminal time of the perturbed problem, and allows for an asymptotic analysis in the new variables.

TL;DR: The theorem of Bayes provides a starting point for the application of statistical considerations and information theory to the analysis of the structures of real decision procedures and allows a rather consistent and simple comparison of most decision procedures.