Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

Grace Wahba

doi:10.1137/0714044

Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

SIAM Journal on Numerical Analysis ◽

10.1137/0714044 ◽

1977 ◽

Vol 14 (4) ◽

pp. 651-667 ◽

Cited By ~ 527

Author(s):

Grace Wahba

Keyword(s):

Linear Operator ◽

Approximate Solutions ◽

Operator Equations ◽

Linear Operator Equations

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Chebyshev Polynomial Iterations and Approximate Solutions of Linear Operator Equations

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/484 ◽

1994 ◽

Vol 13 (4) ◽

pp. 667-681

Author(s):

A.P. Zabrejko ◽

Petr Zabrejko

Keyword(s):

Linear Operator ◽

Chebyshev Polynomial ◽

Approximate Solutions ◽

Operator Equations ◽

Linear Operator Equations

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2. Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind

Optimal Methods for Ill-Posed Problems ◽

10.1515/9783110577211-002 ◽

2018 ◽

pp. 15-30

Keyword(s):

Linear Operator ◽

Approximate Solutions ◽

Operator Equations ◽

Linear Operator Equations

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Theory of reproducing kernels: Applications to approximate solutions of bounded linear operator equations on Hilbert spaces

Selected Papers on Analysis and Differential Equations - American Mathematical Society Translations: Series 2 ◽

10.1090/trans2/230/06 ◽

2010 ◽

pp. 107-134 ◽

Cited By ~ 19

Author(s):

Saburou Saitoh

Keyword(s):

Linear Operator ◽

Hilbert Spaces ◽

Bounded Linear Operator ◽

Approximate Solutions ◽

Reproducing Kernels ◽

Operator Equations ◽

Bounded Linear ◽

Linear Operator Equations

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A class of approximate solutions to linear operator equations

Journal of Approximation Theory ◽

10.1016/0021-9045(73)90112-3 ◽

1973 ◽

Vol 9 (1) ◽

pp. 61-77 ◽

Cited By ~ 25

Author(s):

Grace Wahba

Keyword(s):

Linear Operator ◽

Approximate Solutions ◽

Operator Equations ◽

Linear Operator Equations

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The method of consistent approximation for solving non-linear operator equations

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(78)90187-8 ◽

1978 ◽

Vol 18 (3) ◽

pp. 242-245

Author(s):

Yu.L. Gaponenko

Keyword(s):

Linear Operator ◽

Operator Equations ◽

Consistent Approximation ◽

Non Linear ◽

Non Linear Operator ◽

Linear Operator Equations

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Numerical approximation of linear operator equations using a generalized Fourier series: ordinary and partial differential equations with boundary conditions

Applied Mathematical Modelling ◽

10.1016/0307-904x(89)90207-2 ◽

1989 ◽

Vol 13 (10) ◽

pp. 601-614 ◽

Cited By ~ 2

Author(s):

Theodore V. Hromadka ◽

Robert J. Whitley

Keyword(s):

Fourier Series ◽

Partial Differential Equations ◽

Linear Operator ◽

Differential Equations ◽

Boundary Conditions ◽

Numerical Approximation ◽

Operator Equations ◽

Partial Differential ◽

Generalized Fourier Series ◽

Linear Operator Equations

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On nonnegative solvability of linear operator equations

Integral Equations and Operator Theory ◽

10.1007/bf01225214 ◽

1994 ◽

Vol 18 (1) ◽

pp. 88-108 ◽

Cited By ~ 2

Author(s):

Ruey-Jen Jang-Lewis ◽

Harold Dean Victory

Keyword(s):

Linear Operator ◽

Operator Equations ◽

Linear Operator Equations

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Optimal Error Estimates for Linear Operator Equations

ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique - Numerical Mathematics / Numerische Mathematik ◽

10.1007/978-3-0348-6285-1_7 ◽

1979 ◽

pp. 97-106

Author(s):

W. Krabs

Keyword(s):

Linear Operator ◽

Error Estimates ◽

Optimal Error Estimates ◽

Operator Equations ◽

Optimal Error ◽

Linear Operator Equations

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Applications to Linear Operator Equations

The Best Approximation Method in Computational Mechanics ◽

10.1007/978-1-4471-2020-9_8 ◽

1993 ◽

pp. 222-237

Author(s):

Theodore V. Hromadka

Keyword(s):

Linear Operator ◽

Operator Equations ◽

Linear Operator Equations

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On the Convergence of Regularization Methods for Ill-Posed Linear Operator Equations

Improperly Posed Problems and Their Numerical Treatment ◽

10.1007/978-3-0348-5460-3_6 ◽

1983 ◽

pp. 81-95 ◽

Cited By ~ 10

Author(s):

Heinz W. Engl

Keyword(s):

Linear Operator ◽

Regularization Methods ◽

Operator Equations ◽

Ill Posed ◽

Linear Operator Equations

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