A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind

William J. Kammerer; M. Zuhair Nashed

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1971)

  • Volume: 51, Issue: 1-2, page 20-25
  • ISSN: 0392-7881

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Kammerer, William J., and Nashed, M. Zuhair. "A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 51.1-2 (1971): 20-25. <http://eudml.org/doc/296100>.

@article{Kammerer1971,
author = {Kammerer, William J., Nashed, M. Zuhair},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {7},
number = {1-2},
pages = {20-25},
publisher = {Accademia Nazionale dei Lincei},
title = {A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind},
url = {http://eudml.org/doc/296100},
volume = {51},
year = {1971},
}

TY - JOUR
AU - Kammerer, William J.
AU - Nashed, M. Zuhair
TI - A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1971/7//
PB - Accademia Nazionale dei Lincei
VL - 51
IS - 1-2
SP - 20
EP - 25
LA - eng
UR - http://eudml.org/doc/296100
ER -

References

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  1. CIMMINO, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari, «La Ricerca Scientifica», Roma, Serie II, 326-333 (1938). 
  2. VOTRUBA, G. F., Generalized Inverses and Singular Equations in Functional Analysis, Ph. D. Dissertation, University of Michigan, Ann Arbor, 1963. MR2614652
  3. PENROSE, R., A generalized inverse for matrices, «Proc. Camb. Phil. Soc.», 51, 406-413 (1955). Zbl0065.24603MR69793
  4. PENROSE, R., On best approximate solutions of linear matrix equations, «Proc. Camb. Phil. Soc.», 52, 17-19 (1956). Zbl0070.12501MR74092
  5. TRICOMI, F., Integral Equations, Interscience, New York, 1957. Zbl0078.09404MR94665
  6. MIKHLIN, S. G. and SMOLITSKIY, K. L., Approximate Methods for Solution of Differential and Integral Equations, American Elsevier, New York, 1967. MR218019
  7. KELLER, H. B., The solution of singular and semidefinite linear systems by iteration, «SIAM J. Numer. Anal.», 2, 281-290 (1965). Zbl0135.37503MR195244
  8. PETRYSHYN, W. V., On generalized inverses and uniform convergence of ( I - β K ) n with applicatipns to iterative methods, «J. Math. Anal. Appl.», 18, 417-439 (1967). Zbl0189.47502MR208381DOI10.1016/0022-247X(67)90036-4
  9. ARGHIRIADE, E., Sur l'inverse généralisée d'un operateur linéaire dans les espaces de Hilbert, «Rend. Acc. dei Lincei», 45, fasc. 6, 471-477 (1968). Zbl0186.45103MR247440
  10. ARGHIRIADE, E. and DRAGOMIR, A., Remarques sur quelques theorems relatives à l'inverse généralisée d'un operateur linéaire dans les espaces de Hilbert, «Rend. Acc. dei Lincei», 46, fasc. 4, 333-338 (1969). Zbl0186.45104MR256140
  11. KÄMMERER, W. J. and NASHED, M. Z., Steepest descent for singular linear operators with nonclosed range, «Applicable Analysis», 1143-159 (1971). Zbl0212.15802MR290134DOI10.1080/00036817108839011
  12. KÄMMERER, W. J. and NASHED, M. Z., On the convergence of the conjugate gradient method for singular linear operator equations, «SIAM J. Numer. Analysis», to appear. MR319368DOI10.1137/0709016
  13. SHOWALTER, D. W. and BEN-ISRAEL, A., Representation and computation of the generalized inverse of a bounded linear operator between two Hilbert spaces, «Rend. Acc. dei Lincei», 48, fasc. 2, 184-194 (1970). Zbl0202.41703MR273432

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