E1AR0002@SMUVM1.BITNET (08/22/86)
Max Benson Assistant Professor of Computer Science University of Minnesota-Duluth !ihnp4!umn-cs!umd-cs!max -or- max%umn-duluth@csnet-relay ---------------------------------------------------------------------- %A Linda Deneen %A Gary Shute %T Polygonizations of Point Sets in the Plane %R 86-9 %I University of Minnesota-Duluth %C Duluth, Minnesota %D July, 1986 %X This paper examines the problem of finding the different ways that a set of $n$ points in the plane can be connected to form a simple polygon. Such a connection is called a polygonalization. Because the number arbitrary polygonizations can be exponential in $n$, attention is restricted to a special class of polygonizations, those that are nondegenerate and star-shaped. An algorithm and data structure for determining the nondegenerate star-shaped polygonalizations of a set of $n$ points in the plane is described. The running time of this algorithm is shown to be $O(n^5)$. %A Max Benson %T ENVIRONMENTS: An Algebraic Computing Technique %R 86-10 %I University of Minnesota-Duluth %C Duluth, Minnesota %D July, 1986 %X An environment is a representation of an algebraic structure within a program by a data structure and associated primitives. This paper describes a programming technique and its implementation in the C language based on environments. The programmer can encode algorithms in algebra by setting up the environment and then making high level calls on primitives for natural algebraic operations. An example of working program written using this technique is given which computes the Todd polynomials $T_n(y;c_1,\ldots,c_n)$. __________________________________________________________________________ CENTRE FOR MATHEMATICS AND COMPUTER SCIENCE Postbus 4079 1009 AB Amsterdam The Netherlands CMCS Department of Numerical Mathematics reports 1985 Listed below is a list of 1985 publications of our Department of Numerical Mathematics. These reports are available on exchange basis for your reports or other publications on corresponding subjects. However, please do not send any reprints. They are also available from our Sales Department. The prices of the documents - subject to change without prior notice - are given in Dutch currency. Foreign payments are subject to a surcharge per remittance to cover bank, postal and handling charges. Where appropriate you will be invoiced with your order. If you wish to obtain any of these reports, please encircle the issues that you are interested in and return this list. Please add your name and address on this list. Ordering through electronic mail can be done by sending to rob@mcvax.uucp April 1986 Report NM-R8501 f 3,90 B. P. Sommeijer, P. J. van der Houwen & B. Neta Symmetric linear multistep methods for second-order differential equations with periodic solutions. Amsterdam, C.W.I., 1985 (9 p.) Report NM-R8502 f 3,90 H. Arndt, P. J. van der Houwen & B. P. Sommeijer Numerical integration of retarded differential equations with periodic solutions. Amsterdam, C.W.I., 1985 (11 p.) Report NM-R8503 f 6,30 H. J. J. te Riele Computation of all the amicable pairs below 10 . Amsterdam, C.W.I., 1985 (42 p.) Report NM-R8504 f 3,90 P. J. van der Houwen & B. P. Sommeijer Explicit Runge-Kutta (-Nystr"om) methods with reduced phase errors for computing oscillating solutions. Amsterdam, C.W.I., 1985 (17 p.) Report NM-R8505 f 3,90 P. W. Hemker & S. P. Spekreijse Multigrid solution of the steady Euler equations. Amsterdam, C.W.I., 1985 (13 p.) Report NM-R8506 f 3,90 J. G. Verwer Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines. Amsterdam, C.W.I., 1985 (15 p.) Report NM-R8507 f 3,90 P. W. Hemker & S. P. Spekreijse Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations. Amsterdam, C.W.I., 1985 (17 p.) Report NM-R8508 f 3,90 B. P. Sommeijer On the economization of explicit Runge-Kutta methods. Amsterdam, C.W.I., 1985 (17 p.) Report NM-R8509 f 3,90 P. J. van der Houwen & B. P. Sommeijer Predictor-corrector methods for periodic second-order initial value problems. Amsterdam, C.W.I., 1985 (17 p.) Report NM-R8510 f 3,90 P. J. van der Houwen Discretization of hyperbolic differential equations with periodic solutions. Amsterdam, C.W.I., 1985 (5 p.) Report NM-R8511 f 3,90 F. W. Wubs Performance evaluation of explicit shallow-water equations solver on the Cyber 205. Amsterdam, C.W.I., 1985 (12 p.) Report NM-R8512 f 3,90 J. Kok Two ADA mathematical functions packages for use in real time. Amsterdam, C.W.I., 1985 (9 p.) Report NM-R8513 f 3,90 J. H. M. ten Thije Boonkkamp & J. G. Verwer On the odd-even hopscotch scheme for the numerical integration of time-dependent partial differential equations. Amsterdam, C.W.I., 1985 (15 p.) Report NM-R8514 f 3,90 P. J. van der Houwen Spatial discretization of hyperbolic equations with periodic solutions. Amsterdam, C.W.I., 1985 (15 p.) Report NM-R8515 f 3,90 J. van de Lune, H. J. J. te Riele & D. T. Winter On the zeros of the Riemann zeta function in the critical strip, IV. Amsterdam, C.W.I., 1985 (18 p.) Report NM-R8516 f 3,90 W. H. Hundsdorfer Stability and B-convergence of linearly implicit Runge-Kutta. methods Amsterdam, C.W.I., 1985 (16 p.) Report NM-R8517 f 3,90 K. Burrage, W. H. Hundsdorfer & J. G. Verwer A study of B-convergence of Runge-Kutta methods. Amsterdam, C.W.I., 1985 (15 p.) Report NM-R8518 f 3,90 W. M. Lioen NUMVEC FORTRAN library manual. Chapter: elliptic PDEs : routine: MGZEB. Amsterdam, C.W.I., 1985 (17 p.) Report NM-R8519 f 3,90 P. J. van der Houwen & B. P. Sommeijer Reduction of dispersion in hyperbolic difference schemes by adapting the space discretization. Amsterdam, C.W.I., 1985 (12 p.) Report NM-R8520 f 3,90 S. P. Spekreijse Second order accurate upwind solutions of the 2D steady Euler equations by the use of a defect correction method. Amsterdam, C.W.I., 1985 (16 p.) Report NM-R8521 f 3,90 F. W. Wubs Stabilization of explicit methods for hyperbolic initial-value problems. Amsterdam, C.W.I., 1985 (12 p.) Report NM-R8522 f 5,10 J. G. Blom & H. Brunner The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods. Amsterdam, C.W.I., 1985 (28 p.) Report NM-R8523 f 3,90 P. W. Hemker Defect correction and higher order schemes for the multigrid solution of the steady Euler equations. Amsterdam, C.W.I., 1985 (14 p.) Report NM-R8524 f 3,90 M. Louter-Nool BLAS on the CYBER 205. Amsterdam, C.W.I., 1985 (24 p.) Report NM-R8525 f 3,90 J. M. Sanz-Serna, J. G. Verwer & W. H. Hundsdorfer Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations. Amsterdam, C.W.I., 1985 (12 p.) _ |_| Please send us the reports marked above on exchange basis. _ |_| Please send us the reports marked above with an invoice Institution: ............................................................... Address : ............................................................... ............................................................... ............................................................... Date : ............................. ......................... (signature)