Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations

M. Z. Nashed; Grace Wahba

doi:10.1137/0505095

Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/0505095 ◽

1974 ◽

Vol 5 (6) ◽

pp. 974-987 ◽

Cited By ~ 75

Author(s):

M. Z. Nashed ◽

Grace Wahba

Keyword(s):

Linear Operator ◽

Reproducing Kernel ◽

Generalized Inverses ◽

Operator Equations ◽

Reproducing Kernel Spaces ◽

Linear Operator Equations

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The exact solution of system of linear operator equations in reproducing kernel spaces

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.03.036 ◽

2008 ◽

Vol 203 (1) ◽

pp. 56-61 ◽

Cited By ~ 10

Author(s):

Zhong Chen ◽

Zhi-jie Chen

Keyword(s):

Exact Solution ◽

Linear Operator ◽

Reproducing Kernel ◽

Operator Equations ◽

Reproducing Kernel Spaces ◽

Linear Operator Equations

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Regularization and approximation of linear operator equations in reproducing kernel spaces

Bulletin of the American Mathematical Society ◽

10.1090/s0002-9904-1974-13684-0 ◽

1974 ◽

Vol 80 (6) ◽

pp. 1213-1219 ◽

Cited By ~ 31

Author(s):

M. Z. Nashed ◽

Grace Wahba

Keyword(s):

Linear Operator ◽

Reproducing Kernel ◽

Operator Equations ◽

Reproducing Kernel Spaces ◽

Linear Operator Equations

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Some Iterative Methods for Linear Operator Equations with Applications to Generalized Inverses

SIAM Journal on Applied Mathematics ◽

10.1137/0132049 ◽

1977 ◽

Vol 32 (3) ◽

pp. 610-618 ◽

Cited By ~ 1

Author(s):

L. J. Lardy

Keyword(s):

Linear Operator ◽

Iterative Methods ◽

Generalized Inverses ◽

Operator Equations ◽

Linear Operator Equations

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Perturbations and Approximations for Generalized Inverses and Linear Operator Equations

Generalized Inverses and Applications ◽

10.1016/b978-0-12-514250-2.50013-5 ◽

1976 ◽

pp. 325-396 ◽

Cited By ~ 35

Author(s):

M. Zuhair Nashed

Keyword(s):

Linear Operator ◽

Generalized Inverses ◽

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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