Theorems on M-splittings of a singular M-Matrix which depend on graph structure
From MaRDI portal
Publication:2266566
DOI10.1016/0024-3795(84)90222-2zbMath0561.65020OpenAlexW2050488651MaRDI QIDQ2266566
Publication date: 1984
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0024-3795(84)90222-2
Inequalities involving eigenvalues and eigenvectors (15A42) Iterative numerical methods for linear systems (65F10)
Related Items
The convergence of the modified Gauss--Seidel methods for consistent linear systems ⋮ An analysis of convergence for two-stage waveform relaxation methods ⋮ On a matrix identity connecting iteration operators associated with a \(p\)-cyclic matrix ⋮ Block iterative algorithms for stochastic matrices ⋮ On graph compatible splittings of M-matrices ⋮ Inverse \(M\)-matrix inequalities and generalized ultrametric matrices ⋮ On a two-level multigrid solution method for finite Markov chains ⋮ On the convergence of splittings for a \(Z\)-matrix ⋮ On Accelerated Iterative Methods for the Solution of Systems of Linear Equations ⋮ Characterizations and classifications of M-matrices using generalized nullspaces ⋮ On upper triangular block weak regular splittings of a singular \(M\)-matrix ⋮ The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method ⋮ On regular splittings of an M-matrix ⋮ Splittings ofM-operators: Irreducibility and the index of the iteration operator ⋮ Characterizations of singular irreducible M-matrices ⋮ A conjecture concerning the Hadamard product of inverses of \(M\)-matrices ⋮ Even order uniform hypergraph via the Einstein product ⋮ Comparison of three classes of algorithms for the solution of the linear complementarity problem with an \(H_+\)-matrix ⋮ Comparison results of the preconditioned AOR methods for \(L\)-matrices ⋮ Vector-borne disease models with Lagrangian approach ⋮ On algebraic Riccati equations associated with regular singular \(M\)-matrices ⋮ On computation of the steady-state probability distribution of probabilistic Boolean networks with gene perturbation ⋮ Weak-convergence theory of quasi-nonnegative splittings for singular matrices. ⋮ On algebraic Riccati equations associated with \(M\)-matrices ⋮ Cyclic convergence of iterative methods in Markov modelling ⋮ Block Gauss elimination followed by a classical iterative method for the solution of linear systems. ⋮ On the choice of parameters in MAOR type splitting methods for the linear complementarity problem ⋮ Preconditioned Gauss-Seidel type iterative method for solving linear systems ⋮ On Stein-Rosenberg type theorems for nonnegative and Perron-Frobenius splittings ⋮ Generalizations of \(M\)-matrices which may not have a nonnegative inverse ⋮ \(H\)-splittings and two-stage iterative methods ⋮ Convergence and comparisons of waveform relaxation methods for initial value problems of linear ODE systems ⋮ Some results on preconditioned mixed-type splitting iterative method ⋮ On the convergence of the discretized multi-splitting waveform relaxation algorithm ⋮ On regular splittings and graph compatible splittings of an \(M\)-matrix ⋮ On parallel multisplitting iterative methods for singular linear systems ⋮ Comparison results for parallel multisplitting methods with applications to AOR methods ⋮ New convergence results for alternating methods ⋮ Convergence of parallel multisplitting iterative methods for M-matrices ⋮ Some applications of spectral theory of nonnegative matrices to input-output models ⋮ Safe bounds for the solutions of nonlinear problems using a parallel multisplitting method ⋮ On Nekrasov matrices ⋮ Some results on a generalized alternating iterative method ⋮ The relationship of a regular splitting to a graph compatible splitting ⋮ Parallel interval multisplittings ⋮ Convergent Iterations for Computing Stationary Distributions of Markov Chains ⋮ Two new modified Gauss-Seidel methods for linear system with M-matrices ⋮ Inverses of Perron complements of inverse \(M\)-matrices ⋮ Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices ⋮ Inverse tridiagonalZ-Martices∗ ⋮ On the periodicity of the graph of nonnegative matrices ⋮ Modified iterative methods for linear sustems of equations ⋮ Comparisons of spectral radii and the theorem of Stein-Rosenberg ⋮ Resolvents of minus \(M\)-matrices and splittings of \(M\)-matrices ⋮ Modified iterative methods for consistent linear systems ⋮ Iterative algorithms for large stochastic matrices ⋮ Pseudoirreducible and pseudoprimitive bounded operators ⋮ On the spectral properties of \(M\)-matrices and its applications ⋮ A product index theorem with applications to splittings of \(M\)-matrices ⋮ Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices ⋮ On the convergence of iterative methods for solving singular linear systems
Cites Work
- Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen
- Bounds on the indices of the spectral-circle eigenvalues of a nonnegative matrix
- Theorems of Stein-Rosenberg type. III. The singular case
- Algebraic eigenspaces of nonnegative matrices
- M-matrices leading to semiconvergent splittings
- The concepts of irreducibility and full indecomposability of a matrix in the works of Frobenius, König and Markov
- Convergent nonnegative matrices and iterative methods for consistent linear systems
- On the singular graph and the Weyl characteristic of an M-matrix
- Generalized inverse-positivity and splittings of M-matrices
- Convergent Regular Splittings for Singular M-Matrices
- Matrix Methods for Queuing Problems
- Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems
- Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods
- An Inequality for Latent Roots Applied To Determinants with Dominant Principal Diagonal
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item