Convergence of Newton-like methods for singular operator equations using outer inverses

DOI10.1007/BF01385696zbMath0797.65047OpenAlexW2054204520MaRDI QIDQ1326480

Xiaojun Chen, M. Zuhair Nashed

Publication date: 13 October 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133761

zbMATH Keywords

Banach spacessemilocal convergenceNewton-like methodsouter inverseMysovskii theoremssemilocal Kantorovich-type convergence theoremssingular derivatives

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

A Newton’s iteration converges quadratically to nonisolated solutions too, A parameterized Newton method and a quasi-Newton method for nonsmooth equations, A two-step iterative method and its acceleration for outer inverses, A continuous orbit for the generalized inverse, Moore–Penrose inverse and group inverse, Perturbation analysis of Moore-Penrose quasi-linear projection generalized inverse of closed linear operators in Banach spaces, Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey, Perturbation analysis of generalized inverses of linear operators in Banach spaces, Innovation based on Gaussian elimination to compute generalized inverse \(A_{T,S}^{(2)}\), Newton's Method for Underdetermined Systems of Equations Under the γ-Condition, A direct Newton method for calculus of variations, Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices, Local convergence results of Gauss--Newton's like method in weak conditions, A verification method for solutions of nonsmooth equations, A generalized transversality in global analysis, Representation and approximate for generalized inverse \(A_{T,S}^{(2)}\): revisited, Computing the outer and group inverses through elementary row operations, Parametric method for global optimization, Weighted G-Outer Inverse of Banach Spaces Operators, Additive perturbations and multiplicative perturbations for the core inverse of bounded linear operator in Hilbert space, Some new perturbation theorems for generalized inverses of linear operators in Banach spaces, A unified approach for the convergence of certain numerical algorithms, using recurrent functions, Newton-type method for solving generalized inclusion, Inexact Newton-type methods, Local convergence of a secant type method for solving least squares problems, Gauss-Newton method for solving linear inverse problems with neural network coders, Partial Newton-correction method for multiple fixed points of semi-linear differential operators by Legendre-Gauss-Lobatto pseudospectral method, \( (P,Q)-{\varepsilon} \)-pseudo condition spectrum for \(2\times 2\) matrices. Linear operator and application, Common properties among various generalized inverses and constrained binary relations, Core–EP Star and Star Core–EP Operators, A minimal norm corrected underdetermined Gauß-Newton procedure, Perturbation and expression for inner inverses in Banach spaces and its applications, Computation of outer inverses of tensors using the QR decomposition, Continuous homogeneous selections of set-valued metric generalized inverses of linear operators in Banach spaces, Majorizing sequences for iterative methods, Modified SMS method for computing outer inverses of Toeplitz matrices, On the Gauss-Newton method, New proofs of two representations and minor of generalized inverse \(A_{T,S}^{(2)}\), On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces, Perturbations and expressions for generalized inverses in Banach spaces and Moore-Penrose inverses in Hilbert spaces of closed linear operators, A new augmented singular transform and its partial Newton-correction method for finding more solutions, On stable perturbations for outer inverses of linear operators in Banach spaces, Near subnormal operators and subnormal operators, Full-rank representations of outer inverses based on the QR decomposition, Majorizing sequences for iterative procedures in Banach spaces, A derivative free iterative method for solving least squares problems, Comments on some recent results concerning \(\{2,3\}\) and \(\{2,4\}\)-generalized inverses, Outer inverses and multi body system simulation, Convergence analysis of least-squares collocation methods for nonlinear higher-index differential-algebraic equations, Convergence rates of a multilevel method for the regularization of nonlinear ill-posed problems, Rank theorems of operators between Banach spaces, Characterizations and representations of the \((P, Q)\)-outer generalized inverse, Newton-Type Solvers Using Outer Inverses for Singular Equations, Complete rank theorem of advanced calculus and singularities of bounded linear operators, An efficient computation of generalized inverse of a matrix, Three classes of smooth Banach submanifolds in \(B(E,F)\), A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonvariational quasilinear elliptic PDEs, The representation and computation of generalized inverse \(A^{(2)}_{T,S}\), Lavoie inequalities for weighted generalized inverses of matrices, Extended Newton-type method for nonlinear functions with values in a cone, Parametric proximal-point methods, Continuity of generalized inverses of linear operators in Banach spaces and its applications, (T,S) splitting methods for computing the generalized inverse and rectangular systems^∗, Criteria for the metric generalized inverse and its selections in Banach spaces, Rank equalities related to outer inverses of matrices and applications, A Convergence Analysis of Newton-Like Method for Singular Equations Using Recurrent Functions, Further results on iterative methods for computing generalized inverses, Fixed points for operators with generalized Hölder derivative, Condition numbers for the outer inverse and constrained singular linear system, The Kantorovich theorem and interior point methods, New conditions for the convergence of Newton-like methods and applications, Topological and geometric property of matrix algebra, A Parametric Newton Method for Optimization Problems in Hilbert Spaces, A rank theorem of operators between Banach spaces, Compute lim_{λ → 0}X(λI_p+YAX)⁻¹Yby the product singular value decomposition, On the perturbation and subproper splittings for the generalized inverse \(A_{T,S}^{(2)}\) of rectangular matrix \(A\), Relaxing the convergence conditions for Newton-like methods, Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces, On the perturbation of outer inverses of linear operators in Banach spaces, On the convergence of inexact two-step Newton-like algorithms using recurrent functions, Local convergence theorems of Newton's method for nonlinear equations using outer or generalized inverses, The Representation and Computational Procedures for the Generalized Inverse of an OperatorAin Hilbert Spaces, A note on the perturbation of an outer inverse, A higher order iterative method for \(A^{(2)}_{T,S}\), A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications, Two closed novel formulas for the generalized inverse \(A_{T,S}^{(2)}\) of a complex matrix with given rank, Newton—type methods under regular smoothness, Toward Global Convergence for Strongly Nonlinear Ill-Posed Problems via a Regularizing Multilevel Approach, Adaptive strategy for the damping parameters in an iteratively regularized Gauss-Newton method, Weaker convergence criteria for Traub's method, The smooth Banach submanifold \(B^*(E,F)\) in \(B(E,F)\), Efficient regularized Newton-type algorithm for solving convex optimization problem, Convergence of Gauss-Newton's method and uniqueness of the solution, On broyden's method for the regularization of nonlinear ill-posed problems, High-order iterative methods for the DMP inverse, New versions of Newton method: step-size choice, convergence domain and under-determined equations, Iterative Regularization and Generalized Discrepancy Principle for Monotone Operator Equations, Historical developments in convergence analysis for Newton's and Newton-like methods, The theory of Newton's method, The representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\), An augmented singular transform and its partial Newton method for finding new solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Kantorovich-type convergence analysis for the Gauss-Newton-method
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• A convergence theorem for Newton-like methods in Banach spaces
• Starlike domains of convergence for Newton's method at singularities
• A Newton-Raphson method for the solution of systems of equations
• Convergence of the Newton process to multiple solutions
• On Newton-like methods
• Extension of Newton's method to nonlinear functions with values in a cone
• Convergence Rates for Newton’s Method at Singular Points
• On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
• Inner, outer, and generalized inverses in banach and hilbert spaces
• Convergence domains of certain iterative methods for solving nonlinear equations
• Uniqueness of the solution in a Kantorovich-type theorem of Häu\ler for the Gauss-Newton Method
• Approximations to Generalized Inverses of Linear Operators
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Introduction to Numerical Continuation Methods