Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A simplicial mapping method for locating the zeros of a function


Authors: C. S. Hsu and W. H. Zhu
Journal: Quart. Appl. Math. 42 (1984), 41-59
MSC: Primary 65H05
DOI: https://doi.org/10.1090/qam/736504
MathSciNet review: 736504
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The currently available methods of finding the zeros of a vector function are quite effective but they do require a prior knowledge of the approximate locations of the zeros. Such a knowledge is, however, often not available, hence making the task of finding the zeros very difficult. Developed in this paper is a method which enables us to search the whole domain of interest in a systematic way to locate all the simple zeros approximately. This method complements naturally the various conventional iteration procedures. The method involves (i) partitioning the domain into a system of simplexes and (ii) at each simplex examining a local simplicial mapping induced by the given function in order to test whether a zero is present. Special properties of the barycentric coordinates are used in devising a simple testing procedure which makes the method viable and effective.


References [Enhancements On Off] (What's this?)

  • [1] P. S. Aleksandrov, Combinatorial topology, Vol. 1, Graylock Press, Rochester, N.Y., 1956 MR 0076324
  • [2] K. M. Brown, A quadratically convergent Newton-like method based upon Gaussian elimination, SIAM J. Numer. Anal. 6, 560-569 (1969) MR 0263229
  • [3] S. S. Cairns, Introductory topology, Ronald Press, New York, 1968 MR 0243508
  • [4] B. Carnahanm H. A. Luther and H. O. Wilkes, Applied numerical methods, Wiley, New York, 1969
  • [5] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955 MR 0069338
  • [6] C. S. Hsu, A theory of index for dynamical systems of order higher than two, J. Appl. Mech., 47, 421-427 (1980) MR 574234
  • [7] C. S. Hsu and W. H. Leung, Singular entities and an index theory for cell functions, J. Math. Anal. Appl. (to appear) MR 739959
  • [8] S. Lefschetz, Introduction to topology, Princeton University Press, Princeton, N.J., 1949 MR 0031708
  • [9] K. Nomizu, Fundamentals of linear algebra, McGraw-Hill, New York, 1966 MR 0234963
  • [10] S. Perlis, Theory of matrices, Addison-Wesley, Reading, Mass., 1952 MR 0048384

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65H05

Retrieve articles in all journals with MSC: 65H05


Additional Information

DOI: https://doi.org/10.1090/qam/736504
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society