Mathematical Programming: Series A and B
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Parallel Splitting Method for Coupled Monotone Inclusions
SIAM Journal on Control and Optimization
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Inconsistent signal feasibility problems: least-squares solutionsin a product space
IEEE Transactions on Signal Processing
Fixed Points of Averages of Resolvents: Geometry and Algorithms
SIAM Journal on Optimization
Fixed Points of Averages of Resolvents: Geometry and Algorithms
SIAM Journal on Optimization
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To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century, when Carl Friedrich Gauss developed the method of least squares of a system of linear equations—its solutions can be viewed as fixed points of averaged projections onto hyperplanes. A powerful generalization of this problem is to find fixed points of averaged resolvents (i.e., firmly nonexpansive mappings). This paper concerns the relationship between the set of fixed points of averaged resolvents and certain fixed point sets of compositions of resolvents. It partially extends recent work for two mappings on a question of C. Byrne. The analysis suggests a reformulation in a product space. Algorithmic consequences are also presented.