Convergence and comparison theorems for single and double decompositions of rectangular matrices

DOI10.1007/s10092-013-0079-3zbMath1318.65017OpenAlexW1967392140MaRDI QIDQ2017958

Sabyasachi Pani, Litismita Jena, Debasisha Mishra

Publication date: 23 March 2015

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-013-0079-3

zbMATH Keywords

comparison theoremiterative methodMoore-Penrose inversematrix splittingproper splittingconvergence theoremdouble splittingnon-negativity

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Iterative numerical methods for linear systems (65F10)

Related Items (17)

Proper nonnegative splittings over proper cones of rectangular matrices ⋮ More on proper nonnegative splittings of rectangular matrices ⋮ Index-proper nonnegative splittings of matrices ⋮ Properweak regular splitting and its application to convergence of alternating iterations ⋮ Some comparison theorems for proper weak splittings of type II ⋮ Extensions of theory of regular and weak regular splittings to singular matrices ⋮ Additional Results on Convergence of Alternating Iterations Involving Rectangular Matrices ⋮ Comparison results for proper nonnegative splittings of matrices ⋮ Two-stage iterations based on composite splittings for rectangular linear systems ⋮ Singular \(M\)-matrices which may not have a nonnegative generalized inverse ⋮ Alternating stationary iterative methods based on double splittings ⋮ On convergence of two-stage iterative scheme ⋮ Three-step alternating and preconditioned scheme for rectangular matrices ⋮ On comparison theorems for splittings of different semimonotone matrices ⋮ A note on index-proper multisplittings of matrices ⋮ Convergence theory of iterative methods based on proper splittings and proper multisplittings for rectangular linear systems ⋮ Comparison results for proper double splittings of rectangular matrices

Cites Work

• Comparison theorems for a subclass of proper splittings of matrices
• Comparisons of regular splittings of matrices
• A note on double splittings of different monotone matrices
• Comparisons of weak regular splittings and multisplitting methods
• Operator inequalities
• 3-Part splittings for singular and rectangular linear systems
• Iterative methods for least-square problems based on proper splittings.
• Applications of Perron-Frobenius theory to population dynamics
• Generalized inverses. Theory and applications.
• Convergence and comparison theorems for double splittings of matrices
• Estimation of the Optimum Relaxation Factors in Partial Factorization Iterative Methods
• Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods
• Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems
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