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Investigating an overdetermined system of linear equations by using convex functions

Yıl 2017, Cilt: 46 Sayı: 5, 865 - 874, 01.10.2017

Öz

The paper studies the application of convex functions in order to prove the existence of optimal solutions of an overdetermined system of linear
equations. The study approaches the problem by using even convex functions instead of projections. The research also relies on some special
properties of unbounded convex sets, and the lower level sets of continuous functions.

Kaynakça

  • P. Bloomeld, W. Steiger, Least Absolute Deviations: Theory, Applications and Algorithms, Birkhauser Basel, 1983.
  • M. Fiedler, J. Nedoma, J. Ramik, J. Rohn, K. Zimmermann, Linear Optimization Problems with Inexact Data, Springer-Verlag US, 2006.
  • B. Grünbaum, Convex Polytopes (Second Edition), Springer-Verlag, New York, 2003.
  • C. P. Niculescu, L. E. Persson, Convex Functions and Their Applications, Springer Science+ Business Media New York, 2006.
  • M. R. Osborne, Finite Algorithms in Optimization and Data Analysis, John Wiley & Sons New York, 1985.
  • R. W. Owens, V. P. Sreedharan, Algorithms for solving overdetermined systems of linear equations in the lp-metric, 0 < p < 1, J. Approx. Theory, 24 (1978), 1-17.
  • Z. Pavi¢, Extension of Jensen's inequality to ane combinations, J. Inequal. Appl., 2014 (2014), Article ID 298.
  • Z. Pavi¢, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl., 2015 (2015), Article ID 222.
  • A. W. Roberts, D. E. Varberg, Convex Functions, Academic Press New York and London, 1973.
  • J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999.
  • C. Udrişte, Convex Functions and Optimization Methods on Riemannian Manifolds, Kluwer Academic Publishers, Dordrecht, 1994.
  • G. Williams, Overdetermined systems of linear equations, Amer. Math. Monthly, 97 (1990), 511-513.
Yıl 2017, Cilt: 46 Sayı: 5, 865 - 874, 01.10.2017

Öz

Kaynakça

  • P. Bloomeld, W. Steiger, Least Absolute Deviations: Theory, Applications and Algorithms, Birkhauser Basel, 1983.
  • M. Fiedler, J. Nedoma, J. Ramik, J. Rohn, K. Zimmermann, Linear Optimization Problems with Inexact Data, Springer-Verlag US, 2006.
  • B. Grünbaum, Convex Polytopes (Second Edition), Springer-Verlag, New York, 2003.
  • C. P. Niculescu, L. E. Persson, Convex Functions and Their Applications, Springer Science+ Business Media New York, 2006.
  • M. R. Osborne, Finite Algorithms in Optimization and Data Analysis, John Wiley & Sons New York, 1985.
  • R. W. Owens, V. P. Sreedharan, Algorithms for solving overdetermined systems of linear equations in the lp-metric, 0 < p < 1, J. Approx. Theory, 24 (1978), 1-17.
  • Z. Pavi¢, Extension of Jensen's inequality to ane combinations, J. Inequal. Appl., 2014 (2014), Article ID 298.
  • Z. Pavi¢, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl., 2015 (2015), Article ID 222.
  • A. W. Roberts, D. E. Varberg, Convex Functions, Academic Press New York and London, 1973.
  • J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999.
  • C. Udrişte, Convex Functions and Optimization Methods on Riemannian Manifolds, Kluwer Academic Publishers, Dordrecht, 1994.
  • G. Williams, Overdetermined systems of linear equations, Amer. Math. Monthly, 97 (1990), 511-513.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Zlatko Pavic Bu kişi benim

Vedran Novoselac Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 5

Kaynak Göster

APA Pavic, Z., & Novoselac, V. (2017). Investigating an overdetermined system of linear equations by using convex functions. Hacettepe Journal of Mathematics and Statistics, 46(5), 865-874.
AMA Pavic Z, Novoselac V. Investigating an overdetermined system of linear equations by using convex functions. Hacettepe Journal of Mathematics and Statistics. Ekim 2017;46(5):865-874.
Chicago Pavic, Zlatko, ve Vedran Novoselac. “Investigating an Overdetermined System of Linear Equations by Using Convex Functions”. Hacettepe Journal of Mathematics and Statistics 46, sy. 5 (Ekim 2017): 865-74.
EndNote Pavic Z, Novoselac V (01 Ekim 2017) Investigating an overdetermined system of linear equations by using convex functions. Hacettepe Journal of Mathematics and Statistics 46 5 865–874.
IEEE Z. Pavic ve V. Novoselac, “Investigating an overdetermined system of linear equations by using convex functions”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 5, ss. 865–874, 2017.
ISNAD Pavic, Zlatko - Novoselac, Vedran. “Investigating an Overdetermined System of Linear Equations by Using Convex Functions”. Hacettepe Journal of Mathematics and Statistics 46/5 (Ekim 2017), 865-874.
JAMA Pavic Z, Novoselac V. Investigating an overdetermined system of linear equations by using convex functions. Hacettepe Journal of Mathematics and Statistics. 2017;46:865–874.
MLA Pavic, Zlatko ve Vedran Novoselac. “Investigating an Overdetermined System of Linear Equations by Using Convex Functions”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 5, 2017, ss. 865-74.
Vancouver Pavic Z, Novoselac V. Investigating an overdetermined system of linear equations by using convex functions. Hacettepe Journal of Mathematics and Statistics. 2017;46(5):865-74.