7. Interval Matrices
Society for Industrial and Applied Mathematics eBooks · 2009
Previous chapter Next chapter Other Titles in Applied Mathematics Introduction to Interval Analysis7. Interval Matricespp.85 - 103Chapter DOI:https://doi.org/10.1137/1.9780898717716.ch7PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutExcerpt 7.1 Definitions By an interval matrix, we mean a mean a matrix whose elements are interval numbers. For example, we might have A= ( A11 A12 A21 A22 ) = ( [1,2] [−1,1] [0,4] [6,8] ) . 7.1 If A is an interval matrix with elements Aij and B is a matrix with real elements Bij such that Bij ∈ Aij for all i and j, then we write B ∈ A. Matrix Norm, Width, and Midpoint We use the matrix norm ‖A‖ = max i ∑ j | Aij | 7.2 for an interval matrix A. This is an interval extension of the maximum row sum norm for real matrices. If B is any real matrix contained in an interval matrix A, then ‖B‖ ≤ ‖A‖. We define the width w (A) of an interval matrix A by w (A) = max i,j w ( Aij ) . 7.3 The midpoint of A is the real matrix m (A) whose elements are the midpoints of the corresponding elements of A: (m (A) )ij =m ( Aij ) . Clearly, m (A) ∈ A. Previous chapter Next chapter RelatedDetails Published:2009ISBN:978-0-89871-669-6eISBN:978-0-89871-771-6 https://doi.org/10.1137/1.9780898717716Book Series Name:Other Titles in Applied MathematicsBook Code:OT110Book Pages:ix + 213Key words:interval analysis, scientific computing, automatic result verification, bounding ranges, numerical analysis