Computer Engineering Commons^™

A New Differential Formalism For Interval-Valued Functions And Its Potential Use In Detecting 1-D Landscape Features, Vladik Kreinovich, Hung T. Nguyen, Gracaliz Pereira Dimuro, Antonio Carlos Da Rocha Costa, Benjamin Rene Callejas Bedregal

Departmental Technical Reports (CS)

In many practical problems, it is important to know the slope (derivative) dy/dx of one quantity y with respect to some other quantity x. For example, different 1-D landscape features can be characterized by different values of the derivative dy/dx, where y is an altitude, and x is a horizontal coordinate. In practice, we often know the values of y(x) for different x with interval uncertainty. How can we then find the set of possible values of the slope? In this paper, we formulate this problem of differentiating interval-values functions in precise terms, and we describe an (asymptotically) optimal algorithm …

Real-Time Algorithms For Statistical Analysis Of Interval Data, Berlin Wu, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

When we have only interval ranges [xi] of sample values x1,...,xn, what is the interval [V] of possible values for the variance V of these values? There are quadratic time algorithms for computing the exact lower bound V- on the variance of interval data, and for computing V+ under reasonable easily verifiable conditions. The problem is that in real life, we often make additional measurements. In traditional statistics, if we have a new measurement result, we can modify the value of variance in constant time. In contrast, previously known algorithms for processing interval data required that, once a new data …

A Full Function-Based Calculus Of Directed And Undirected Intervals: Markov's Interval Arithmetic Revisited, Juergen Wolff Von Gudenberg, Vladik Kreinovich

Departmental Technical Reports (CS)

This paper proposes a new interpretation of intervals as classes of functions having the same domain. Interval operations are seen as operations on these classes. This approach allows to recover Markov's directed interval arithmetic by taking into account the monotonicity of the functions.

Probabilities, Intervals, What Next? Optimization Problems Related To Extension Interval Computations To Situations With Partial Information About Probabilities, Vladik Kreinovich

Departmental Technical Reports (CS)

When we have only interval ranges [xi-,xi+] of sample values x1,...,xn, what is the interval [V-,V+] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V+ is NP-hard. We provide a feasible (quadratic time) algorithm for computing the exact lower bound V- on the variance of interval data. We also provide feasible algorithms that computes V+ under reasonable easily verifiable conditions, in particular, in case interval uncertainty is introduced to maintain privacy in a statistical database.

We also extend the main formulas of interval arithmetic for different arithmetic operations …