DOI10.1017/CBO9780511526473zbMath0715.65030MaRDI QIDQ3998722
Arnold Neumaier
Publication date: 17 September 1992
Properties of the Solution Set of Absolute Value Equations and the Related Matrix Classes,
Nash Equilibrium Points for Generalized Matrix Game Model with Interval Payoffs,
Existence verification for singular and nonsmooth zeros of real nonlinear systems,
Pseudozeros of multivariate polynomials,
Verified Error Bounds for All Eigenvalues and Eigenvectors of a Matrix,
Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation,
Inner and outer estimations of the generalized solution sets and an application in economic,
Interval extensions of the Halley method and its modified method for finding enclosures of roots of nonlinear equations,
Linear System of Equations with Doubly Stochastic Interval Coefficient Matrix,
Inverse of a fuzzy matrix of fuzzy numbers,
On the Solution of Parametrised Linear Systems,
Verified Solutions of Systems of Nonlinear Polynomial Equations,
Interval Methods for Global Optimization Using the Boxing Method,
A Branch-and-Prune Method for Global Optimization,
Traditional Parameter Estimation Versus Estimation of Guaranteed Parameter Sets,
Verified Determination of Singularities in Chemical Processes,
On the algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic,
Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems,
Floating-point arithmetic,
Generalized Perron Roots and Solvability of the Absolute Value Equation,
A note on checking regularity of interval matrices,
Tight computationally efficient approximation of matrix norms with applications,
Various approaches to multiobjective linear programming problems with interval costs and interval weights,
Robot workspace approximation with modified bicentered Krawczyk method,
Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders,
Interval‐valued variational programming problem with Caputo–Fabrizio fractional derivative,
Reference-point-based branch and bound algorithm for multiobjective optimization,
Strong regularity of parametric interval matrices,
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A new interval diagnosis method: Application to the spacecraft rendezvous phase of the Mars sample return mission,
A Branch--and--Bound-Based Algorithm for Nonconvex Multiobjective Optimization,
The Worst Case Finite Optimal Value in Interval Linear Programming,
The united stable solution set of interval continuous-time algebraic Riccati equation and veri ed numerical computation of its outer estimation,
Robust Designs for Circle Coverings of a Square,
Bounding error of calculating the matrix functions,
Mathematically Rigorous Global Optimization and Fuzzy Optimization,
ON ARITHMETIC OPERATIONS OF INTERVAL NUMBERS,
Generating Feasible Points for Mixed-Integer Convex Optimization Problems by Inner Parallel Cuts,
Self-validating methods,
Quasiconvex relaxations based on interval arithmetic,
Computational error bounds for multiple or nearly multiple eigenvalues,
Effective topological degree computation based on interval arithmetic,
OPTIMAL INVESTMENT STRATEGY VIA INTERVAL ARITHMETIC,
A Finite Algorithm for Almost Linear Complementarity Problems,
Formally certified floating-point filters for homogeneous geometric predicates,
On solvability recognition for interval linear systems of equations,
A NOTE ON DEFINITIONS OF THE RANK FOR INTERVAL MATRICES,
An extension of the \(\alpha\mathrm{BB}\)-type underestimation to linear parametric Hessian matrices,
Enclosing Chebyshev Expansions in Linear Time,
Determinants of Interval Matrices,
Rigorous solution of linear programming problems with uncertain data,
Generalization of real interval matrices to other fields,
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How do you compute the midpoint of an interval?,
Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics,
Weak and Strong Compatibility in Data Fitting Problems Under Interval Uncertainty,
Reliable Computation of the Singularities of the Projection in $$\mathbb R^3$$ of a Generic Surface of $$\mathbb R^4$$,
Eigenvalues, pseudospectrum and structured perturbations,
AE solutions to two-sided interval linear systems over max-plus algebra,
Efficient polyhedral enclosures for the reachable set of nonlinear control systems,
Error bounds for complementarity problems with tridiagonal nonlinear functions,
Hybrid theoretical, experimental and numerical study of vibration and buckling of composite shells with scatter in elastic moduli,
On computability and triviality of well groups,
Propagating systems of dense linear integer constraints,
Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation \(A(p)X=B(p)\),
A database of rigorous and high-precision periodic orbits of the Lorenz model,
Error bounds for mixed integer nonlinear optimization problems,
Interval finite difference method for steady-state temperature field prediction with interval parameters,
Application of the Krawczyk-Moore-Jones algorithm to electric circuit analysis and its further development,
Fast verified solutions of linear systems,
Direct methods for linear systems with inexact input data,
Verified numerical computation for nonlinear equations,
Numerical existence proof of five solutions for certain two-transistor circuit equations,
On verified numerical computations in convex programming,
Computer algebra for guaranteed accuracy. How does it help?,
Maximum consistency method for data fitting under interval uncertainty,
Reliable modeling and optimization for chemical engineering applications: Interval analysis approach,
Uncertainty in thermal basin modeling: an interval finite element approach,
Rigorous enclosures of rotation numbers by interval methods,
Interval Monte Carlo as an alternative to second-order sampling for estimating ecological risk,
Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis,
Super-fast validated solution of linear systems,
Interval methods for verifying structural optimality of circle packing configurations in the unit square,
Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics,
Theoretical convergence analysis of a general division-deletion algorithm for solving global search problems,
Solving interval constraints by linearization in computer-aided design,
Interval finite elements as a basis for generalized models of uncertainty in engineering mechanics,
Linear systems with large uncertainties, with applications to truss structures,
Formulation for reliable analysis of structural frames,
Univex interval-valued mapping with differentiability and its application in nonlinear programming,
Interval bounds on the solutions of semi-explicit index-one DAEs. I: Analysis,
Interval bounds on the solutions of semi-explicit index-one DAEs. II: Computation,
Exponential stability of interval dynamical systems with quadratic nonlinearity,
On interval systems \([x = [A][x] + [b]\) and the powers of interval matrices in complex interval arithmetics],
Constraint propagation on quadratic constraints,
Principal component analysis on interval data,
Interval linear systems: the state of the art,
On smooth reformulations and direct non-smooth computations for minimax problems,
Nonsmooth exclusion test for finding all solutions of nonlinear equations,
Universal algorithms for solving the matrix Bellman equations over semirings,
An interval extension based on occurrence grouping,
Multiple/arbitrary precision interval computations in C-XSC,
A comparison of verified distance computation between implicit objects using different arithmetics for range enclosure,
On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach,
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse,
An algorithm for computing a neighborhood included in the attraction domain of an asymptotically stable point,
Error bounds for nonlinear complementarity problems with band structure,
An interval algorithm for multi-objective optimization,
On a computer-aided approach to the computation of Abelian integrals,
Extended interval Newton method based on the precise quotient set,
Fast interval matrix multiplication,
Rigorous filtering using linear relaxations,
On interval enclosures using slope arithmetic,
Interval Ostrowski-type methods with guaranteed convergence,
Generalized McCormick relaxations,
Efficient solution of a class of quantified constraints with quantifier prefix exists-forall,
Interval methods for model qualification: methodology and advanced application,
On approximation of the best case optimal value in interval linear programming,
Upper bounding in inner regions for global optimization under inequality constraints,
Interval-based projection method for under-constrained numerical systems,
Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof,
A reinforcement learning approach to interval constraint propagation,
Global optimization of generalized semi-infinite programs using disjunctive programming,
Reverse propagation of McCormick relaxations,
Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard,
Preconditioning linearized equations,
Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions,
Bounds for the solutions of absolute value equations,
On certain computable tests and componentwise error bounds,
A comparison of some methods for bounding connected and disconnected solution sets of interval linear systems,
A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices,
Differentiable McCormick relaxations,
Interval arithmetic operations for uncertainty analysis with correlated interval variables,
Interval arithmetic over finitely many endpoints,
On the properties of Sard kernels and multiple error estimates for bounded linear functionals of bivariate functions with application to non-product cubature,
Theoretical rate of convergence for interval inclusion functions,
A new framework for sharp and efficient resolution of NCSP with manifolds of solutions,
A branch and bound algorithm for numerical Max-CSP,
A generalization of Hukuhara difference and division for interval and fuzzy arithmetic,
Testing pseudoconvexity via interval computation,
An interval extension of SMS method for computing weighted Moore-Penrose inverse,
The influence of interval arithmetic on the shape of uncertainly defined domains modelled by closed curves,
Symbolic interval inference approach for subdivision direction selection in interval partitioning algorithms,
Comparison between Baumann and admissible simplex forms in interval analysis,
Rigorous parameter reconstruction for differential equations with noisy data,
A framework for existence tests based on the topological degree and homotopy,
New methods for calculating \(\alpha\)BB-type underestimators,
Slope enclosures for functions given by two or more branches,
Components identification based method for box constrained variational inequality problems with almost linear functions,
Uncertainty analysis for heat convection-diffusion problem with large uncertain-but-bounded parameters,
Enclosing all zeros of an analytic function - a rigorous approach,
Efficient handling of universally quantified inequalities,
Efficient task scheduling in the parallel result-verifying solution of nonlinear systems,
A contribution to the feasibility of the interval Gaussian algorithm,
A method for outer interval solution of systems of linear equations depending linearly on interval parameters,
Some results in interval multiobjective linear programming for recognizing different solutions,
Numerical enclosures of the optimal cost of the Kantorovitch's mass transportation problem,
On the solution sets of particular classes of linear interval systems,
Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory,
The cluster problem in multivariate global optimization,
Safe starting regions by fixed points and tightening,
Box-splitting strategies for the interval Gauss-Seidel step in a global optimization method,
Enclosing solutions of linear interval equations is NP-hard,
On a class of enclosure methods for initial value problems,
Enclosing solutions of an inverse Sturm-Liouville problem with finite data,
A new concept of fixed point in metric and normed interval spaces,
The computational complexity of approximating the minimal perturbation scaling to achieve instability in an interval matrix,
A combined method for enclosing all solutions of nonlinear systems of polynomial equations,
Enclosing the solution set of parametric interval matrix equation \(A(p)X = B(p)\),
Verified solution of large systems and global optimization problems,
Maximum compatibility method for data fitting under interval uncertainty,
A parallel complex zero finder,
Finding all solutions of nonlinearly constrained systems of equations,
On the selection of subdivision directions in interval branch-and-bound methods for global optimization,
A branch-and-bound algorithm for bound constrained optimization problems without derivatives,
Eigenvector sets for intervals of matrices,
A numerically rigorous proof of curve veering in an eigenvalue problem for differential equations,
Checking robust nonsingularity of tridiagonal matrices in linear time,
On parameter loci of the Hénon family,
Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of Kaucher arithmetic,
On the computational complexity of the solution of linear systems with moduli,
Enclosing solutions of overdetermined systems of linear interval equations,
A computational study of global optimization solvers on two trust region subproblems,
A sufficient condition for non-overestimation in interval arithmetic,
Improved iteration schemes for validation algorithms for dense and sparse nonlinear systems,
Beyond the Melnikov method. II: Multidimensional setting,
Certificates of infeasibility via nonsmooth optimization,
Is an interval the right result of arithmetic operations on intervals?,
Some properties of the lower bound of optimal values in interval convex quadratic programming,
Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers,
Low redundancy polynomial checks for numerical computation,
The adaptive convexification algorithm for semi-infinite programming with arbitrary index sets,
Global optimization of disjunctive programs,
A certified branch \& bound approach for reliability-based optimization problems,
Interval solution of nonlinear equations using linear programming,
Invertibility properties of singular integral operators associated with the Lamé and Stokes systems on infinite sectors in two dimensions,
A new approach to obtain algebraic solution of interval linear systems,
raSAT: an SMT solver for polynomial constraints,
Efficient solution of interval optimization problem,
A new method for computing a \(p\)-solution to parametric interval linear systems with affine-linear and nonlinear dependencies,
A new algorithm for Chebyshev minimum-error multiplication of reduced affine forms,
A generalization of the classical \(\alpha \)BB convex underestimation via diagonal and nondiagonal quadratic terms,
Ten methods to bound multiple roots of polynomials,
Lower bound functions for polynomials,
Domain reduction techniques for global NLP and MINLP optimization,
Convex and concave relaxations for the parametric solutions of semi-explicit index-one differential-algebraic equations,
Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems,
A proof of Jones' conjecture,
Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation,
Estimation of the sensitivity of linear and nonlinear algebraic problems,
A geometric approach for computing a posteriori error bounds for the solution of a linear system,
Decompostition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems,
Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation,
On the solution of interval linear systems,
Epsilon-inflation with contractive interval functions,
What can interval analysis do for global optimization?,
Some remarks on two interval-arithmetic modifications of the Newton method,
\(H\)-splittings and two-stage iterative methods,
Safety verification of non-linear hybrid systems is quasi-decidable,
Bounding the set of solutions of a perturbed global optimization problem,
Exclusion regions for optimization problems,
First order rejection tests for multiple-objective optimization,
Approximating a solution set of nonlinear inequalities,
Bounds for eigenvalues of parameter-dependent matrices,
A new approach to interval-valued probability measures, a formal method for consolidating the languages of information deficiency: foundations,
Rank one interval enclosure of the parametric united solution set,
Interval tensors and their application in solving multi-linear systems of equations,
Complexity issues for the symmetric interval eigenvalue problem,
A computer-assisted proof of symbolic dynamics in Hyperion's rotation,
Central configurations in planar \(n\)-body problem with equal masses for \(n=5,6,7\),
Finding all solutions of a class of nonlinear equations using an improved LP test,
Quasi-decidability of a fragment of the first-order theory of real numbers,
Solving interval systems of equations obtained during the numerical solution of boundary value problems,
Convergent upper bounds in global minimization with nonlinear equality constraints,
Solving interval linear least squares problems by PPS-methods,
Linear interval parametric approach to testing pseudoconvexity,
Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY,
On interval portfolio selection problem,
Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations,
A general branch-and-bound framework for continuous global multiobjective optimization,
On preconditioning and solving an extended class of interval parametric linear systems,
Solving fully interval linear systems of equations using tolerable solution criteria,
Validated solutions of initial value problems for ordinary differential equations,
Rigorously computed orbits of dynamical systems without the wrapping effect,
Parallel methods for verified global optimization practice and theory,
Rigorous convex underestimators for general twice-differentiable problems,
Bounding the zeros of an interval equation,
Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization,
Interval solutions for interval algebraic equations,
Enhancing numerical constraint propagation using multiple inclusion representations,
Interval propagation and search on directed acyclic graphs for numerical constraint solving,
On proving existence of feasible points in equality constrained optimization problems,
An interval version of PROMETHEE for the comparison of building products' design with ill-defined data on environmental quality,
Structured perturbations and symmetric matrices,
Experiments using interval analysis for solving a circuit design problem,
Global optimization using interval arithmetic,
Accelerating filtering techniques for numeric CSPs,
Inverse optimization: towards the optimal parameter set of inverse LP with interval coefficients,
Computing the noncentral-\(F\) distribution and the power of the \(F\)-test with guaranteed accuracy,
Interval unions,
Representation of analysis results involving aleatory and epistemic uncertainty,
Solving systems of linear fuzzy equations by parametric functions -- an improved algorithm,
Rigorous Numerical Study of Low-Period Windows for the Quadratic Map,
RESPONSE STATISTICS OF LINEAR STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS UNDER GAUSSIAN STOCHASTIC INPUT,
Solving minimax problems by interval methods,
Guaranteed parameter set estimation for exponential sums: the three-terms case,
A new robust algorithm to trace curves,
Extension of the Hansen-Bliek method to right-quantified linear systems,
On Relation Between P-Matrices and Regularity of Interval Matrices,
Interval Linear Algebra and Computational Complexity,
First steps towards more numerical reproducibility,
Estimation of algebraic solution by limiting the solution set of an interval linear system,
On estimating workload in interval branch-and-bound global optimization algorithms,
A branch and bound algorithm for quantified quadratic programming,
Solution sets of interval-valued fuzzy relational equations,
Interval Analysis for Certified Numerical Solution of Problems in Robotics,
Verified Solution Method for Population Epidemiology Models with Uncertainty,
Enclosures for the solution set of parametric interval linear systems,
On the superstability of an interval family of differential-algebraic equations,
On the Hull of the Solution Sets of Interval Linear Equations,
Computation of Algebraic Solutions to Interval Systems Via Systems of Coordinates,
A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations,
Using interval unions to solve linear systems of equations with uncertainties,
On ranges of non-linear operators,
Convergence results for some piecewise linear solvers,
Rigorous packing of unit squares into a circle,
COUNTING LOW-PERIOD CYCLES FOR FLOWS,
Some notes on the solvability conditions for absolute value equations,
Error Estimation for Nonlinear Complementarity Problems via Linear Systems with Interval Data,
Error bounds and a condition number for the absolute value equations,
A note on the convergence of parametrised non-resonant invariant manifolds,
Geometric branch-and-bound methods for constrained global optimization problems,
INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS,
Constructive Interval Disjunction,
Optimal Planning of Distributed Generation via Nonlinear Optimization and Genetic Algorithms,
How to determine basis stability in interval linear programming,
Global optimization of bounded factorable functions with discontinuities,
Solving kinematics problems by efficient interval partitioning,
Checking weak optimality of the solution to linear programming with interval right-hand side,
VALIDATED STUDY OF THE EXISTENCE OF SHORT CYCLES FOR CHAOTIC SYSTEMS USING SYMBOLIC DYNAMICS AND INTERVAL TOOLS,
An efficient algorithm for finding all solutions of separable systems of nonlinear equations,
Efficient interval partitioning-local search collaboration for constraint satisfaction,
An application of interval methods to stock market forecasting,
On sufficient conditions of the injectivity: Development of a numerical test algorithm via interval analysis,
FOUNDATIONS OF FUZZY SET THEORY AND FUZZY LOGIC: A HISTORICAL OVERVIEW,
Computation of Topological Degree Using Interval Arithmetic, and Applications,
Computing the pessimism of inclusion functions,
A verified inexact implicit Runge-Kutta method for nonsmooth ODEs,
Contracting optimally an interval matrix without loosing any positive semi-definite matrix is a tractable problem,
On the solutions of the interval system \([x = [a][x] + [b]\)],
The optimal solution of an interval system of linear algebraic equations,
Using zonotopes for overestimation-free interval least-squares -- some geodetic applications,
Enclosing solutions of singular interval systems iteratively,
Solvability of interval linear equations and data analysis under uncertainty,
NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS,
Complex interval arithmetic using polar form,
Sharpening interval computations,
Interval Householder method for complex linear systems,
Robust control for two-time-scale discrete interval systems,
Improving inter-block backtracking with interval Newton,
AN ENCLOSURE METHOD FOR FREE BOUNDARY PROBLEMS BASED ON A LINEAR COMPLEMENTARITY PROBLEM WITH INTERVAL DATA*,
On tightness and anchoring of McCormick and other relaxations,
A multidimensional interval Newton method,
Computational experience with rigorous error bounds for the Netlib linear programming library,
Analysis and design of robust controllers using the interval Diophantine equation,
Parameter reconstruction for biochemical networks using interval analysis,
Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof,
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Reachability Analysis and Deterministic Global Optimization of DAE Models,
A smoothing and regularization Broyden-like method for nonlinear inequalities,
Interval arithmetic error estimation for the solution of Fredholm integral equation,
Tight Bounds on the Radius of Nonsingularity,
A numerical approach to compute the topology of the apparent contour of a smooth mapping from \(\mathbb{R}^2\) to \(\mathbb{R}^2\),
A Comparison of Metaheurisitics for the Problem of Solving Parametric Interval Linear Systems,
A Comparison of Methods for Solving Parametric Interval Linear Systems with General Dependencies,
Verified bounds for the determinant of real or complex point or interval matrices,
Systematic computer assisted proofs of periodic orbits of Hamiltonian systems,
Existence of Periodic Solutions of the FitzHugh--Nagumo Equations for an Explicit Range of the Small Parameter,
Stability of an interval family of differential-algebraic equations with variable coefficients,
Solving interval linear programming problems with equality constraints using extended interval enclosure solutions,
Second-order sufficient optimality conditions for local and global nonlinear programming,
New results on verified global optimization,
A right-preconditioning process for the formal-algebraic approach to inner and outer estimation of AE-solution sets.,
How strong is strong regularity?,
Interval-affine Gaussian algorthm for constrained systems,
Validated constraints solving --- practicalities, pitfalls, and new developments,
On unbounded tolerable solution sets,
Using geometric interval algebra modeling for improved three-dimensional camera calibration,
Motivations for an arbitrary precision interval arithmetic and the MPFI library,
Second-order bounds for linear recurrences with negative coefficients,
Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks,
A new class of improved convex underestimators for twice continuously differentiable constrained NLPs,
A new inclusion function for optimization: kite -- the one-dimensional case,
Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: spline \(\alpha\)BB underestimators,
A new proof of interval extension of the classic Ostrowski's method and its modified method for computing the enclosure solutions of nonlinear equations,
Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints,
Generation of robust root loci for linear systems with parametric uncertainties in an ellipsoid