Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems

DOI10.1137/0714047zbMath0366.65017OpenAlexW1998209214WikidataQ60162493 ScholiaQ60162493MaRDI QIDQ4142618

Robert J. Plemmons, Carl D. jun. Meyer

Publication date: 1977

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0714047

Mathematics Subject Classification ID

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

Related Items

The Growth of Powers of a Nonnegative Matrix, Multistep matrix splitting iteration preconditioning for singular linear systems, Semiconvergence of parallel multisplitting methods for symmetric positive semidefinite linear systems, A note on formulae for the generalized Drazin inverse of anti-triangular block operator matrices in Banach spaces, Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces, THE ARITHMETIC MEAN METHOD FOR FINDING THE STATIONARY VECTOR OF MARKOV CHAINS, On the solution of singular linear systems of algebraic equations by semiiterative methods, Limit behavior of solutions of singular difference equations, Exact expressions for the Drazin inverse of anti-triangular matrices, Weak-convergence theory of quasi-nonnegative splittings for singular matrices., Perturbation analysis of singular linear systems with arbitrary index., A combined direct-iterative approach for solving large scale singular and rectangular consistent systems of linear equations, On the Drazin inverse of anti-triangular block matrices, Representations for the group inverse of anti-triangular block operator matrices, Theorems of Stein-Rosenberg type. III. The singular case, Variational statements and discretization of the boundary-value problem of elasticity where stress at the boundary is known, PURE JOINT PRODUCTION, INCOME DISTRIBUTION, EMPLOYMENT AND THE EXCHANGE RATE, A characterization of weak-monotone matrices, Development of iterative techniques and extrapolation methods for Drazin inverse solution of consistent or inconsistent singular linear systems, On parallel multisplitting methods for symmetric positive semidefinite linear systems, Comparison results for proper nonnegative splittings of matrices, A Combined Direct-Iterative Method for Certain M-Matrix Linear Systems, Multicomponent transport algorithms for partially ionized mixtures, Theorems on M-splittings of a singular M-Matrix which depend on graph structure, Computing generalized inverses of matrices by iterative methods based on splittings of matrices, Fast linear iterations for distributed averaging, Convergent nonnegative matrices and iterative methods for consistent linear systems, Projective iterative algorithms with application to multicomponent transport, Projected iterative algorithms for complex symmetric systems arising in magnetized multicomponent transport, Generalized inverse-positivity and splittings of M-matrices, MP matrices, Block-iterative methods for consistent and inconsistent linear equations, Convergent regular splittings for nonnegative matrices, On semi-convergence of parameterized Uzawa methods for singular saddle point problems, Successive matrix squaring algorithm for computing the Drazin inverse, More on generalizations of matrix monotonicity, Perturbation analysis of singular linear systems with index one^∗, Semiconvergence criteria of iterations and extrapolated iterations and constructive methods of semiconvergent iteration matrices, The Drazin inverse of anti-triangular block matrices, Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems, Conference celebrating the 60th birthday of Robert J. Plemmons. Papers from the conference, Winston-Salem, NC, USA, January 1999, Dedication to Robert J. Plemmons, Comparison theorems for the convergence factor of iterative methods for singular matrices, On the use of incomplete semiiterative methods for singular systems and applications in Markov chain modeling., On finite element methods for the Neumann problem, Finite precision behavior of stationary iteration for solving singular systems