Continuous dependence of least squares solutions of linear boundary value problems
R. Kannan and John Locker
Proc. Amer. Math. Soc. 59 (1976), 107-110
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Abstract: Let be the unique least squares solution of minimal norm of the linear boundary value problem , where is a selfadjoint differential operator in . Working in the Sobolev space , the alternative method is used to examine the continuous dependence of the on the parameter as , and the convergent and divergent cases are both characterized.
Cesari, Nonlinear analysis, Non-linear mechanics (Centro
Internaz. Mat. Estivo (C.I.M.E.), I Ciclo, Bressanone, 1972), Edizioni
Cremonese, Rome, 1973, pp. 1–95. MR 0407672
J. K. Hale, Applications of alternative problems, Lecture Notes, Brown University, Providence, Rhode Island, 1971.
Locker, On constructing least squares
solutions to two-point boundary value problems, Trans. Amer. Math. Soc. 203 (1975), 175–183. MR 0372303
(51 #8519), http://dx.doi.org/10.1090/S0002-9947-1975-0372303-0
- L. Cesari, Nonlinear analysis, Lecture Notes, C. I. M. E., Bressanone, 1972. MR 0407672 (53:11444)
- J. K. Hale, Applications of alternative problems, Lecture Notes, Brown University, Providence, Rhode Island, 1971.
- J. Locker, On constructing least squares solutions to two-point boundary value problems, Trans. Amer. Math. Soc. 203 (1975), 175-183. MR 0372303 (51:8519)
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