Results 1  10
of
13
Interval Analysis for Guaranteed Nonlinear Parameter and State Estimation
"... This paper presents some tools based on interval analysis for guaranteed nonlinear parameter and state estimation in a boundederror context. These tools make it possible to compute outer (and sometimes inner) approximations of the set of all parameter or state vectors that are consistent with the m ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
This paper presents some tools based on interval analysis for guaranteed nonlinear parameter and state estimation in a boundederror context. These tools make it possible to compute outer (and sometimes inner) approximations of the set of all parameter or state vectors that are consistent with the model structure, measurements and noise bounds.
An Improved Unconstrained Global Optimization Algorithm
, 1996
"... Global optimization is a very hard problem especially when the number of variables is large (greater than several hundred). Recently, some methods including simulated annealing, branch and bound, and an interval Newton's method have made it possible to solve global optimization problems with several ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Global optimization is a very hard problem especially when the number of variables is large (greater than several hundred). Recently, some methods including simulated annealing, branch and bound, and an interval Newton's method have made it possible to solve global optimization problems with several hundred variables. However, this is a small number of variables when one considers that integer programming can tackle problems with thousands of variables, and linear programming is able to solve problems with millions of variables. The goal of this research is to examine the present state of the art for algorithms to solve the unconstrained global optimization problem (GOP) and then to suggest some new approaches that allow problems of a larger size to be solved with an equivalent amount of computer time. This algorithm is then implemented using portable C++ and the software will be released for general use. This new algorithm is given with some theoretical results under which the algorit...
On Hardware Support For Interval Computations And For Soft Computing: Theorems
, 1994
"... This paper provides a rationale for providing hardware supported functions of more than two variables for processing incomplete knowledge and fuzzy knowledge. The result is in contrast to Kolmogorov's theorem in numerical (nonfuzzy) case. ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
This paper provides a rationale for providing hardware supported functions of more than two variables for processing incomplete knowledge and fuzzy knowledge. The result is in contrast to Kolmogorov's theorem in numerical (nonfuzzy) case.
On inverse halftoning: computational complexity and interval computations
 John Hopkins University
, 2005
"... Abstract — We analyze the problem of inverse halftoning. This problem is a particular case of a class of difficulttosolve problems: inverse problems for reconstructing piecewise smooth images. We show that this general problem is NPhard. We also propose a new idea for solving problems of this ty ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract — We analyze the problem of inverse halftoning. This problem is a particular case of a class of difficulttosolve problems: inverse problems for reconstructing piecewise smooth images. We show that this general problem is NPhard. We also propose a new idea for solving problems of this type, including the inverse halftoning problem. Need for halftoning I.
Interval Computations and IntervalRelated Statistical Techniques: Tools for Estimating Uncertainty of the Results of Data Processing and Indirect Measurements
"... In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on [−∆, ∆], and to use the corresponding statistical techniques. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such “interval computations” methods have been developed since the 1950s. In this chapter, we provide a brief overview of related algorithms, results, and remaining open problems.
Statistical Data Processing under Interval Uncertainty: Algorithms and Computational Complexity
 Soft Methods for Integrated Uncertainty Modeling
, 2006
"... Why indirect measurements? In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. Examples of such quantities are the distance to a star and the amount of oil in a given well. Since we cannot measure y directly, a na ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Why indirect measurements? In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. Examples of such quantities are the distance to a star and the amount of oil in a given well. Since we cannot measure y directly, a natural idea is to measure y indirectly. Specifically, we find some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn); this relation may be a simple functional transformation, or complex algorithm (e.g., for the amount of oil, numerical solution to an inverse problem). Then, to estimate y, we first measure the values of the quantities x1,..., xn, and then we use the results �x1,..., �xn of these measurements to to compute an estimate �y for y as �y = f(�x1,..., �xn): �x1 �x2
Interval Computations as an Important Part of Granular Computing: An Introduction
"... This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing.
Computational Complexity of Planning with Discrete Time and Continuous State Variables
"... Traditionally, most planning research in AI was concentrated on systems whose state can be characterized by discretevalued fluents. In many practical applications, however, we want to control systems (like robots) whose state can only be described if we used continuous variables (like coordinates). ..."
Abstract
 Add to MetaCart
Traditionally, most planning research in AI was concentrated on systems whose state can be characterized by discretevalued fluents. In many practical applications, however, we want to control systems (like robots) whose state can only be described if we used continuous variables (like coordinates). Planning for such systems corresponds, crudely speaking, to Level 2 of the planing language PDDL2.1. In this paper, we analyze the computational complexity of such planning problems.
Applications of Interval Computations: An Introduction
, 1995
"... The main goal of this introduction is to make the book more accessible to readers who are not familiar with interval computations: to beginning graduate students, to researchers from related fields, etc. With this goal in mind, this introduction describes the basic ideas behind interval computations ..."
Abstract
 Add to MetaCart
The main goal of this introduction is to make the book more accessible to readers who are not familiar with interval computations: to beginning graduate students, to researchers from related fields, etc. With this goal in mind, this introduction describes the basic ideas behind interval computations and behind the applications of interval computations that are surveyed in the book.
ApplicationMotivated Combinations of Fuzzy, Interval, and Probability Approaches, with Application to Geoinformatics,
"... Abstract—Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval, probabilistic, and fuzzy uncertainty. We provide an overview of relat ..."
Abstract
 Add to MetaCart
Abstract—Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval, probabilistic, and fuzzy uncertainty. We provide an overview of related algorithms, results, and remaining open problems. I. MAIN PROBLEM Why indirect measurements? In many reallife situations, we are interested in the value of a physical quantity y that is dif cult or impossible to measure directly. Examples of such quantities are the distance to a star and the amount of oil in a given well. Since we cannot measure y directly, a natural idea is to measure y indirectly. Speci cally, we nd some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn); this relation may be a simple functional transformation, or complex algorithm (e.g., for the amount of oil, numerical solution to an inverse problem). Then, to estimate y, we rst measure the values of the quantities x1,..., xn, and then we use the results ˜x1,..., ˜xn of these measurements to to compute an estimate ˜y for y as ˜y = f(˜x1,..., ˜xn). ˜x1 ˜x2