Calculating the Best Approximate Solution of an Operator Equation

Convergence Banach Spaces Iterative Method Numerical Examples Generalized Inverse Operator Equation Linear Operator Closed Range Approximation Theory of L. V. Kantorovich Best Approximate Solution Galerkin-Type Method

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (2)

The generalized condition numbers of bounded linear operators in Banach spaces ⋮ Generalized inverses of matrices: a perspective of the work of Penrose

Cites Work

Direct iterative methods for least-squares solutions to singular operator equations
On computing the best least squares solutions in Hilbert space
On the approximate solution of operator equations
Approximate solutions of integral and operator equations
The solution of non-unique linear integral equations
Continuity of the set-valued metric projection
On generalized inverses and on the uniform convergence of $(I-\beta K)_ n$ with application to iterative methods
On direct sum decompositions of Hestenes algebras
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The Generalized Inverse of an Unbounded Linear Operator with Unbounded Constraints
On the Generalized Overrelaxation Method for Operation Equations
On the Extrapolated Jacobi or Simultaneous Displacements Method in the Solution of Matrix and Operator Equations
A Note on an Iterative Method for Generalized Inversion of Matrices
On Iterative Computation of Generalized Inverses and Associated Projections
On Error Bounds for Generalized Inverses
On the Continuity of the Generalized Inverse
On the Concept of a $p-q$ Generalized Inverse of a Matrix
The Galerkin Method for the Numerical Solution of Fredholm Integral Equations of the Second Kind
On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations
Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems
A Collection Method for the Numerical Solution of Integral Equations
On Complementary Manifolds and Projections in Spaces L p and l p
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