Block splittings for the conjugate gradient method

We study the generalized conjugate gradient scheme, based on the k-line and k × k block Jacobi splittings A = M ? N, for solving two-dimensional parabolic and elliptic difference equations $\text{AU =}\text{F}\text{?}$. Here A represents the difference operator ch^α ? h²Δ_h. Computational experiments suggest that the eigenvalues of K: = I ? M^?1N cluster, and that the cluster radii decrease as k or ch^α increases. As is well known, clustering improves convergence of the conjugate gradient iterates. We discuss computational results for k = 4, 8, 16, 32 and for ch^α = 0, h, 2. Moreover, we establish the number and size of eigenvalue clusters for the model problem.     

A note on the recursive enumerability of some classes of recursively enumerable languages

An elementary proof is presented for the fact that the class of infinite recursive languages is not recursively enumerable. Its relevance for contemporary linguistics and computer science is explained.     

A quantitative comparison of three simulation languages: SLAM,GPSS/H,SIMSCRIPT

Three simulation languages are quantitatively compared in a manufacturing job shop environment. Both model size and model run length were varied to obtain data on compilation time, execution time. CPU time, memory time and the rate of change of these variables due to changes in the simulation period.     

A qualitative comparison of three simulation languages: GPSS/H,SLAM, SIMSCRIPT

Simulation languages have proliferated with the increased use of simulation as a method of solving manufacturing and other problems. When selecting a simulation language there are both qualitative and quantitative considerations. This study is a qualitative comparison of the discrete portions of GPSS/H, SLAM and SIMSCRIPT.     

Solutions of the two-dimensional Navier-Stokes equations by Chebyshev expansion methods

The steady two-dimensional Navier-Stokes equations in both the vorticity-stream function and the vorticity-velocity formulation are solved by Chebyshev expansion methods. Numerical experiments for the driven flow in a rectangular cavity and the developing flow in a circular tube at low Reynolds numbers are described.     

Numerical simulation of the 1973 Shikotan (Nemuro-Oki) tsunami

The paper presents the results of numerical simulation of Shikotan (Nemuro-Oki) tsunami of 17 June 1973. Static deformations of the sea bottom are computed for some dimensional dislocation model of the seismic source with the parameters obtained from seismological observations. The computed bottom deformations are used as the initial conditions for the tsunami propagation problem in the ocean with a real bathymetry, which is considered within the framework of linear theory of shallow water. Three variants of tsunami source are examined. Travel time charts and computed mareograms at a number of points of the shoreline are presented. At 4 points, where tide-gauge records are available, the comparison of the computed mareograms with the observed ones is made. It is found that the numerical model can reproduce the basic features of the tsunami of 17 June 1973.     

Computer graphics generated from the iteration of algebraic transformations in the complex plane

Algorithms for the generation of intricate shapes resulting from the iteration of algebraic transformations are presented. A special convergence test makes possible the production of a visually striking class of displayable objects. Several illustrations are chosen as examples of the diversity of forms which result from this technique.     

Sequential calculation of the median

Data collection during discrete event digital simulation may involve sampling either continuous or discrete variables. The most commonly used data collection techniques are sequential in the sense that they do not require storage of each observation. It is this moderation of storage requirements that makes such data collection techniques useful in the output analysis of large scale simulations and in the experimental evaluation of random number generators. For some distributions the same median is superior to the sample mean as an estimator of the population mean. When the sample median is desired it is common to store every observation. These observations are then sorted in order to find the central value. This paper describes a sequential technique that permits the median to be calculated without storing all observations. For example, if 100,000 samples are to be taken, selective storage of 440 observations will permit an exact calculation of the sample median with probability 0.98. If the method fails a warning is provided. Central processor unit (CPU) running time for sequential calculation of the median is competitive with the best sorting algorithms.     

Interactive use of finite element programs—or—how to get more out of your finite element model

The paper outlines the application of sensitivity methods to explore the effect of element changes, or to modify the finite element model of a structure. The sensitivity algorithms for structural applications, initially studied at AEO under ESA contract, are partly implemented at AEO for interactive use in conjunction with the finite element analysis of structures. The algorithms are computationally very efficient and hence suited to interactive use in the design and development of structures. Because of the greater insight into structural behaviour that it can provide, sensitivity analysis might open a new, more efficient and cost effective era in the field of structural design and analysis.     

Experiments on the edited condensed nearest neighbor rule

Tomek's preprocessing scheme is discussed for editing the training set prior to analyzing it by Hart's condensed nearest neighbor technique. Preprocessing was performed by a κ-nearest-neighbor pdf estimation scheme, although other methods are suggested in this paper. The procedure was studied experimentally and was found to achieve a significant reduction in the storage requirements of the CNN method while maintaining approximately the same error rate, or even improving it.     

On the selection of collocation points for the numerical solution of singular integral equations with generalized kernels appearing in elasticity problems

A modification of the collocation method for the numerical solution of Cauchy type singular integral equations with generalized kernels is proposed. In accordance with this modification, although the abscissas and weights used in the numerical integration rule for the approximation of the integrals of the integral equation remain unaltered, yet the collocation points are selected in such a way that the poles of the integrands due not only to the Cauchy principal value part of the kernel, but also to the singularities of the generalized part of the kernel are taken into account. This modification assures the convergence of the method to the correct results since the error terms, usually neglected for the collocation points nearest to the end-points of the integration interval and generally tending to infinity, are now taken into consideration for the selection of the collocation points. The method was applied to the singular integral equations derived for the antiplane and plane elasticity problems of a crack terminating at a bimaterial interface.     

Handsketching as a human factor aspect in graphical interaction

For some years a lot of effort has been put into improving the human-computer interface in CAD-systems. After a short introduction on input problems in design processes, some of this work is reported here as well as a fairly new method, handsketching. In the third part of this paper a special system called CASUS is thoroughly explained from the user's point of view. A fourth part deals with the authors' conviction that psychological theories and methods are necessary in order to create still better interfaces. In the last chapter the system presented with all its interface features is compared to some human factor considerations discussed before. No attention is paid to the fact that very often the quality of work is changed by introducing CAD-systems. Though the designer's situation can be very often improved much more by designing his entire work, this paper lays claim only to designing a tool for the designer's hand.     

Computer display and manipulation of biological molecules

This paper describes a computer model that was designed to investigate the conformation of molecules, macromolecules and subsequent complexes. Utilizing an advanced 3-D dynamic computer display system, the model is sufficiently versatile to accommodate a large variety of molecular input and to generate data for multiple purposes such as visual representation of conformational changes, and calculation of conformation and interaction energy. Molecules can be built on the basis of several levels of information. These include the specification of atomic coordinates and connectivities and the grouping of building blocks and duplicated substructures using symmetry rules found in crystals and polymers such as proteins and nucleic acids. Called AIMS (Ames Interactive Molecular modeling System), the model is now being used to study pre-biotic molecular evolution toward life.     

An advanced start algorithm for all-integer programming

In this paper, we present an all-integer cutting plane technique called the Advanced Start Algorithm (ASA), for solving the all-integer (otherwise linear) programming problem (IP). We develop a good advanced primal-infeasible start based on the optimal solution to the LP relaxation, and use a two-stage dual/primal algorithm to obtain the optimal solution to (IP). We illustrate the operation of the ASA on three small problems, and exhibit computational results on a set of standard test problems.     

Speed-varying ol systems

A new type of L system is introduced in which each rule has a “delay”, a word over some alphabet, associated with it. This results in a new characterization of the etol languages, which only partially carries over to the eol languages.     

Vegetation of central Florida's East coast: The distribution of six vegetational complexes of Merritt Island and Cape Canaveral Peninsula

Several discrete vegetation types on Merritt Island and Cape Canaveral barrier island were delineated by use of LANDSAT satellite data. Categories of vegetation based upon community structure and the presence or absence of water were determined in a two-stage analysis. First, a detailed map covering 52 km² was prepared using conventional methods (i.e., site visits, high-resolution aerial photographs, and direct aerial investigations). Then an interactive computerized system (Image 100) was used to analyze LANDSAT data for the same area. Six plant community forms, differing by vegetation height, canopy openness and the amount of water visible from the air, were mapped. These physiognomic characteristics were used because they often influenced the light reflected from an area more than did the floristic composition. The computer was adjusted to detect all regions with similar light-reflectance characteristics; the search limits were then manually adjusted until the regions detected by the computer agreed with the known distribution of vegetation appearing in the detailed vegetation map. These limits were applied to the entire coastal area and the computer maps printed. The resulting distribution maps were spot checked for accuracy by site visitation. The areas identified by the method were indicative of discrete physiognomic types which in turn were easily related to major plant association types. Expression of the computer classification technique's full potential depends on the intimate participation of trained botanists, and the prior completion of extensive field studies.