Matrix interval monotonicity

Why Monotonicity in Interval Computations ?

Monotonicity of functions has been successfully used in many problems of interval computations. However, in the context of interval computations, monotonicity seems somewhat ad hoc. In this paper, we show that monotonicity can be reformulated in interval terms and is, therefore, a natural condition for interval mathematics. One of the main problems of interval computations it to compute the ran...

An Interval Constraint Propagation Algorithm Exploiting Monotonicity

When a function f is monotonic w.r.t. x in a given box, it is well-known that the monotonicity-based interval extension of f computes a sharper image than the natural interval extension does. Indeed, the overestimation due to the variable x with multiple occurrences in f disappears. However, monotonicity has not been exploited in interval filtering/contraction algorithms for solving systems of ...

Exploiting Monotonicity in Interval Constraint Propagation

We propose in this paper a new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), that exploits monotonicity of functions. The propagation is standard, but the Mohc-Revise procedure, used to filter/contract the variable domains w.r.t. an individual constraint, uses monotonic versions of the classical HC4-Revise and BoxNarrow procedures. Mohc-Revise appears to b...

On matrix estimation under monotonicity constraints

Abstract: We consider the problem of estimating an unknown n1×n2 matrix θ∗ from noisy observations under the constraint that θ∗ is nondecreasing in both rows and columns. We consider the least squares estimator (LSE) in this setting and study its risk properties. We show that the worst case risk of the LSE is n−1/2, up to multiplicative logarithmic factors, where n = n1n2 and that the LSE is mi...

Gauss elimination algorithm for interval matrix