Über Struktur und Abschätzungen der Lösungsmenge von linearen Gleichungssystemen mit Intervallkoeffizienten

DOI10.1007/BF02316910zbMath0255.65014OpenAlexW29604136MaRDI QIDQ2558739

Helmut Beeck

Publication date: 1972

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02316910

Mathematics Subject Classification ID

Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (23)

Direct methods for linear systems with inexact input data ⋮ Maximum compatibility method for data fitting under interval uncertainty ⋮ Maximum consistency method for data fitting under interval uncertainty ⋮ Approximate linear algebra is intractable ⋮ Unnamed Item ⋮ Estimates of the solution set of nonlinear equations with uncertain parameters ⋮ New characterizations for the solution set to interval linear systems of equations ⋮ Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of Kaucher arithmetic ⋮ Characterization of AE solution sets of parametric linear systems based on the techniques of convex sets ⋮ On the solution set of a linear equation with the right-hand side and operator given by intervals ⋮ Determination of minimum sets of the set of zeros of a function ⋮ Transformations of mixed solution types of interval linear equations system with boundaries on its left-hand side to linear inequalities with binary variables ⋮ Computational methods of linear algebra ⋮ Zur scharfen Außenabschätzung der Lösungsmenge bei linearen Intervallgleichungssystemen ⋮ The optimal solution of an interval system of linear algebraic equations ⋮ Solving interval linear least squares problems by PPS-methods ⋮ Ein Verfahren zur Behandlung von Ausgleichsaufgaben mit Intervallkoeffizienten ⋮ On solvability recognition for interval linear systems of equations ⋮ Ein Abbruchkriterium für das intervallarithmetische Gesamt- und Einzelschrittverfahren ⋮ Interval analytic treatment of convex programming problems ⋮ Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem ⋮ Interval analysis: Theory and applications ⋮ Three short descriptions of the symmetric and of the skew-symmetric solution set

Cites Work

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• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• Stability of solutions of linear algebraic systems
• On the solution of linear algebraic equations with interval coefficients
• A computer-oriented representation of matrices
• Interval Arithmetic in Matrix Computations, Part I
• Automatic Controlled Precision Calculations
• On the Solution Set of a Linear System with Inaccurate Coefficients
• Zusammenfassender Bericht. Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme
• Admissible Solutions of Linear Systems with Not Sharply Defined Coefficients
• On the Compatibility of a Given Solution With the Data of a Linear System
• Interval Arithmetic in Matrix Computations, Part II

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