Pacific Journal of Mathematics

Proof of the fundamental theorem on implicit functions by use of composite gradient corrections.

William L. Hart and Theodore S. Motzkin

Article information

Source
Pacific J. Math., Volume 8, Number 3 (1958), 429-436.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103039889

Mathematical Reviews number (MathSciNet)
MR0101899

Zentralblatt MATH identifier
0089.03601

Subjects
Primary: 26.00
Secondary: 65.00

Citation

Hart, William L.; Motzkin, Theodore S. Proof of the fundamental theorem on implicit functions by use of composite gradient corrections. Pacific J. Math. 8 (1958), no. 3, 429--436. https://projecteuclid.org/euclid.pjm/1103039889


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References

  • [1] E. Goursat, Sur la theorie des functions implicates, Bull. Soc. Math. France 31 (1903), 184-192.Also, cf. Gilbert A. Bliss, Princeton Colloquium Lectures on Mathematics, American Mathematical Society (1913), 16-18.
  • [2] William L. Hart and Theodore S. Motzkin, A composite Newton-Raphson gradient method
  • [3] William L. Hart, Differential equations and implicit functions in infinitelymany variables, Trans. Amer. Math. Soc. 18 (1917), 125-160.
  • [4] William L. Hart, Functions of infinitely many variables in Hilberi space, Trans. Amer. Math. Soc. 22 (1922), 30-50.