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Interval analysis: Theory and applications. (English) Zbl 0995.65056
Summary: We give an overview on applications of interval arithmetic. Among others we discuss verification methods for systems of linear equations, nonlinear systems, the algebraic eigenvalue problem, initial value problems for ordinary differential equations and boundary value problems for elliptic partial differential equations of second-order. We also consider the item software in this field and give some historical remarks.

MSC:
65G30 Interval and finite arithmetic
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
76F10 Shear flows and turbulence
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65G40 General methods in interval analysis
65G20 Algorithms with automatic result verification
65H10 Numerical computation of solutions to systems of equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65N06 Finite difference methods for boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
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