By B. Wanamaker, K. Massey

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When we say that an algorithm is to process an m × n interval matrix A, we understand that the algorithm is given the pair (A ∈ Qm×n , A ∈ Qm×n ) and that the size of the input is L := size(A) + size(A). Whenever we speak about complexity of such algorithm, we mean a function φ(L) counting the number of steps of the corresponding Turing machine as a function of the bit-size L of the input (A, A). Although the literature focuses mainly on the Turing model (and here we also do so), it would be interesting to investigate the behavior of interval-theoretic problems in other computational models, such as the Blum–Shub–Smale (BSS) model for real-valued computing [2] or the quantum model [1].

Whenever we speak about complexity of such algorithm, we mean a function φ(L) counting the number of steps of the corresponding Turing machine as a function of the bit-size L of the input (A, A). Although the literature focuses mainly on the Turing model (and here we also do so), it would be interesting to investigate the behavior of interval-theoretic problems in other computational models, such as the Blum–Shub–Smale (BSS) model for real-valued computing [2] or the quantum model [1]. 2 Functional Problems and Decision Problems Formally, a functional problem F is a function F : {0, 1}∗ → {0, 1}∗ , where {0, 1}∗ is the set of all finite bit-strings.

Focus on Computational Neurobiology, pp. 115–132. Nova Science Publishers, Commack (2004) Interval Linear Algebra and Computational Complexity ˇ Jaroslav Horáˇcek, Milan Hladík and Michal Cerný Abstract This work connects two mathematical fields – computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system, deciding solvability of a linear system, computing inverse matrix, eigenvalues, checking positive (semi)definiteness or stability.