Obtuse cones and Gram matrices with non-negative inverse

DOI10.1016/S0024-3795(01)00284-1zbMath0982.15028MaRDI QIDQ5947466

Andrzej Cegielski

Publication date: 2 April 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Gram matrix\(QR\)-factorizationconvex minimizationnon-negative inverseobtuse cone

Mathematics Subject Classification ID

Factorization of matrices (15A23) Convex programming (90C25) Theory of matrix inversion and generalized inverses (15A09) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (14)

A characterization of cone nonnegativity of Moore-Penrose inverses of unbounded Gram operators ⋮ Particular formulae for the Moore--Penrose inverse of a columnwise partitioned matrix ⋮ Nonnegative Moore--Penrose inverses of Gram operators ⋮ Projection methods for the linear split feasibility problems ⋮ Asymptotics for some proximal-like method involving inertia and memory aspects ⋮ Particular formulae for the Moore-Penrose inverses of the partitioned bounded linear operators ⋮ Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space ⋮ On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix ⋮ Moore-Penrose inverse of a Gram matrix and its nonnegativity ⋮ New representations of the Moore-Penrose inverse of \(2 \times 2\) block matrices ⋮ Reflection-projection method for convex feasibility problems with an obtuse cone ⋮ Residual Selection in A Projection Method for Convex Minimization Problems ⋮ A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators ⋮ Nonnegative Moore-Penrose inverse of Gram matrices in an indefinite inner product space

Cites Work

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• Monotone Gram matrices and deepest surrogate inequalities in accelerated relaxation methods for convex feasibility problems
• Topological proofs for certain theorems on matrices with non-negative elements
• Block-iterative surrogate projection methods for convex feasibility problems
• A method of projection onto an acute cone with level control in convex minimization
• The Relaxation Method for Solving Systems of Linear Inequalities
• The Efficiency of Subgradient Projection Methods for Convex Optimization, Part I: General Level Methods
• The Efficiency of Subgradient Projection Methods for Convex Optimization, Part II: Implementations and Extensions

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