Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Numerical solution of a parabolic free boundary problem arising in statistical decision theory


Author: Gary G. Sackett
Journal: Math. Comp. 25 (1971), 425-434
MSC: Primary 65N35
DOI: https://doi.org/10.1090/S0025-5718-1971-0300473-9
MathSciNet review: 0300473
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A parabolic free boundary problem which arises in a statistical decision setting is reduced to a free boundary problem for the heat equation which is amenable to numerical solution by the method of lines. An algorithm is given and the apparently globally converging results are compared with the asymptotic expansions of H. Chernoff and J. Breakwell.


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

  • [1] John Breakwell & Herman Chernoff, ``Sequential tests for the mean of a normal distribution. II. (large t),'' Ann. Math. Statist., v. 35, 1964, pp. 162-173. MR 28 #1679. MR 0158456 (28:1679)
  • [2] Herman Chernoff, Sequential Tests for the Mean of a Normal Distribution, Fourth Berkeley Sympos. on Math. Statist. and Prob., vol. 1, Univ. of California Press, Berkeley, Calif., 1961, pp. 79-91. MR 24 #A1788. MR 0131941 (24:A1788)
  • [3] Herman Chernoff, ``Sequential tests for the mean of a normal distribution. III. (small t),'' Ann. Math. Statist., v. 36, 1965, pp. 28-54. MR 30 #680. MR 0170442 (30:680)
  • [4] Nguyen Dinh Chi (Thi), ``On a free boundary problem for a parabolic equation,'' Vestnik Moskov. Univ. Ser. Math. Mech., No. 2, 1966, pp. 40-54. (Russian)
  • [5] Erich Rothe, ``Two dimensional parabolic boundary value problems as the limit of one dimensional boundary value problems,'' Math. Ann., v. 102, 1930, pp. 650-670. (German) MR 1512599
  • [6] G. G. Sackett, ``An implicit free boundary problem for the heat equation,'' SIAM J. Numer. Anal., v. 8, 1971. MR 0283423 (44:654)
  • [7] B. Sherman, Some Comments on Free Boundary Problems for Parabolic Equations Arising in Statistical Decision Theory, Rocketdyne Research Report #66-24, 1966.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N35

Retrieve articles in all journals with MSC: 65N35


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0300473-9
Keywords: Free boundary, method of lines, Bayes risk
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society