Showing papers in "Applications of Mathematics in 1978"
TL;DR: A direct projection method for solving systems of linear algebraic equations is described, which is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimizations of a strictly convex function.
Abstract: A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
18 citations
TL;DR: In this paper, the authors extend the Lobatto-Jacobi numerical integration rule to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauche type kernels by reduction to systems of linear equations.
Abstract: The Lobatto-Jacobi numerical integration rule can be extended so as to apply to the numerical evaluation of Cauchy type principal value integrals and the numerical solution of singular intergral equations with Cauchy type kernels by reduction to systems of linear equations. To this end, the integrals in such a singular integral equation are replaced by sums, as if they were regular integrals, after the singular integral equation is applied at appropriately selected points of the integration interval. An application of this method of numerical solution of singular integral equations is made in the case of a problem of the theory of plane elasticity.
17 citations
14 citations
11 citations
TL;DR: In this article, the error bounds for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains are given for simplicial isoparametric elements in $n$-dimensional space.
Abstract: In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in $n$-dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in $L_2$-norm of the method.
11 citations
9 citations
6 citations
TL;DR: In this paper, the authors discuss the boundary conditions of a deformable body under the action of body forces and describe the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary condition.
Abstract: The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as special cases all known classical, bilateral and unilateral boundary conditions. Further, the principle of virtual displacements and the principle of minimum of the potential energy are established and it is shown that these principles are equivalent to the original boundary condition problem.
6 citations
6 citations
6 citations
TL;DR: This paper contains tables of one-sides significance levels for H based on the number of exceeding observations in two samples suitable for testing difference in location of two samples.
Abstract: The rank statistic $H$ based on the number of exceeding observations in two samples is suitable for testing difference in location of two samples. This paper contains tables of one-sides significance levels $P\{H\geq k\}$ for $k=7,8,\ldots, 11; max (2,n-10)
TL;DR: In this paper, the optimization of total setup plus inventory cost of a certain class of the multistage inventory-production systems with the series arranged production stages having generally different production rates, separated by stores from each other, is discussed.
Abstract: This paper deals with the optimization of total setup plus inventory cost of a certain class of the multistage inventory-production systems with the series arranged production stages having generally different production rates, separated by stores from each other. The optimization is made by the choice of lot sizes across an infinite time horizon. The exact cost-optimization algorithm based on the Bellman optimality principle is derived and applied for deriving two lower bounds of the optimal cost of the above class of systems. These lowe bounds improve that derived by Crowston, Wagner and Williams. Two numerical examples are given.