Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Nonlinear segmented function approximation and analysis of line patterns


Author: Donald E. McClure
Journal: Quart. Appl. Math. 33 (1975), 1-37
MSC: Primary 41A45
DOI: https://doi.org/10.1090/qam/463769
MathSciNet review: 463769
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] C. de Boor and J. R. Rice, Least squares cubic spline approximation. I. Fixed knots, Computer Science Dept. Tech. Rept. 20, Purdue University, 1968
  • [2] C. de Boor and J. R. Rice, Least squares cubic spline approximation. II. Variable knots, Computer Science Dept. Tech. Rept. 21, Purdue University, 1968
  • [3] H. G. Burchard, Splines with optimal knots are better, Applicable Anal. 3, 309-319(1974). MR 0399708
  • [4] P. J. Davis, Interpolation and approximation, Blaisdell, Waltham, Mass., 1963 MR 0157156
  • [5] R. E. Esch and W. L. Eastman, Computational methods for best spline function approximation, J. Approximation Theory 2, 85-96 (1969) MR 0240520
  • [6] U. Grenander, Foundations of pattern analysis, Quart. Appl. Math. 27, 1-55 (1969) MR 0250791
  • [7] U. Grenander, A unified approach to pattern analysis, in Advances in computers 10, Academic Press, New York, 1970
  • [8] C. R. Hobby and J. R. Rice, Approximation from a curve of functions, Arch. Rat. Mech. Anal. 24, 91-106 (1967) MR 0209740
  • [9] S. Karlin and Z. Ziegler, Chebyshevian spline functions, SIAM J. Numer. Anal. 3, 514-543 (1966) MR 0216206
  • [10] D. E. McClure, Feature selection for the analysis of line patterns, Center for Computer and Information Sciences and Division of Applied Mathematics Report, Brown University, 1970 MR 2620331
  • [11] D. E. McClure, Optimal and asymptotically efficient quadrature of stochastic integrals, to appear
  • [12] G. Meinardus, Zur Segmentapproximation mit Polynomen, Z. Angew. Math. Mech. 46, 239-246 (1966) MR 0211154
  • [13] G. Meinardus, Approximation of functions: theory and numerical methods, Springer-Verlag, New York, 1967 MR 0217482
  • [14] T. Pavlidis, Linguistic analysis of waveforms, in Software engineering 2 (ed. J. Tou), Academic Press, New York, 1971
  • [15] T. Pavlidis, Waveform segmentation through functional approximation, Department of Electrical Engineering Tech. Rept. 114, Princeton University, 1972
  • [16] G. M. Phillips, Error estimates for best polynomial approximations, in Approximation theory (ed. A. Talbot), Academic Press, New York, 1970 MR 0277970
  • [17] G. Polya, On the mean value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24, 312-324 (1922) MR 1501228
  • [18] M. J. D. Powell, On best $ {L_2}$ spline approximations, Numerische Mathematik, Differentialgleichungen, Approximationstheorie (Tagungen, Oberwolfach, 1966), Birkhäuser, Basel, 1968, 317-338 MR 0267729
  • [19] N. Ream, Approximation errors in diode-function generators, J. Electron. Control 7, 83-96 (1959)
  • [20] N. Ream, Note on ``Approximation of curves by line segments", Math. Comp. 15, 418-419 (1961) MR 0129109
  • [21] J. R. Rice, The approximation of functions, vol. II, Addison-Wesley, Reading, Mass., 1969 MR 0244675
  • [22] J. Sacks and D. Ylvisaker, Designs for regression problems with correlated errors, Ann. Math. Statist. 37, 66-89 (1966) MR 0192601
  • [23] J. Sacks and D. Ylvisaker, Designs for regression problems with correlated errors; many parameters, Ann. Math. Statist. 39, 49-69 (1968) MR 0220424
  • [24] J. Sacks and D. Ylvisaker, Designs for regression problems with correlated errors III, Ann. Math. Statist. 41, 2057-2074 (1970) MR 0270530
  • [25] L. L. Schumaker, Uniform approximation by Tchebycheffian spline functions I: Fixed knots, MRC Tech. Rept. 768, Madison, Wis., 1967 MR 0241866
  • [26] L. L. Schumaker, Uniform approximation by Tchebycheffian spline functions II: Free knots, MRC Tech. Rept. 810, Madison, Wis., 1967 MR 0241867
  • [27] L. L. Schumaker, On the smoothness of best spline approximations, J. Approximation Theory 2, 410-418 (1969) MR 0259438
  • [28] H. Stone, Approximation of curves by line segments, Math. Comp. 15, 40-47 (1961) MR 0119390
  • [29] A. F. Timan, Theory of approximation of functions of a real variable, Pergamon Press, New York, 1963 MR 0192238
  • [30] G. Wahba, On the regression design problem of Sacks and Ylvisaker, Ann. Math. Statist. 42, 1035-1053 (1971) MR 0279955

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 41A45

Retrieve articles in all journals with MSC: 41A45


Additional Information

DOI: https://doi.org/10.1090/qam/463769
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society