Interval Arithmetic Training for beginnersLyngby 24 May 2002 An Interval Arithmetic Training for beginners is organised August 26-28, 2002, in Lyngby, Denmark. The event is a joint effort between the Danish Technical University (DTU) and Sun Microsystems. DTU is the Sun Center of Excellence (COE) for Interval Arithmetic and Dynamic Systems.
An interval is a range of numbers bounded by the interval's endpoints. Interval Arithmetic is the system for performing arithmetic on intervals. The most significant characteristic of interval arithmetic is that resulting intervals are guaranteed to contain the set of all possible results from any interval computation. This is true, even when interval arithmetic is implemented on a computer using finite precision floating-point arithmetic.
As a consequence, interval arithmetic is a new computing paradigm. Almost all the existing rules and assumptions for floating-point computations need to be re-examined.
There is a problem with floating-point numbers: floating-point numbers are logically disconnected from the real worlds of science, engineering, and mathematics. The causes of this disconnect are that a single floating-point number contains no accuracy information. Most real numbers cannot be represented using finite precision floating-point numbers.
The consequences of this disconnect are profound, including that computing speed produces unprecedented opportunities and risks. Unfortunately, without intervals, the opportunities cannot be exploited and the risks cannot be avoided.
Intervals create a tight logical connection between computing and scientific, engineering, and mathematical reality. As a consequence, it becomes possible to:
The interval paradigm has precisely the properties needed to connect computing to the real world. Intervals are tightly connected to the real world in precisely the way that floating-point numbers, alone, are not. The width of an interval can be used to represent error in an approximation. Because an interval represents all the values it contains, a single pair of interval endpoints represents an infinite number of values, or a continuum. It is this fact that connects intervals to mathematics, so that nonlinear problems can be numerically solved. A number is a single numeric value. An interval is a range of numbers, bounded by the interval's endpoints. The width of an interval can be zero, in which case it is a point, or it can be very large. A somewhat more formal definition of Intervals and Interval Arithmetic is the following: "An interval is the set of all real numbers between and including the interval's lower and upper bound. Interval arithmetic is used to evaluate arithmetic expressions over sets of numbers contained in intervals. Any interval arithmetic result is a new interval that is guaranteed to contain the set of all possible resulting values." A simple example is the following. Define two intervals A and B. Assume A = [-1.0000, 2.0000] and B = [1.0000, 2.0000]. We can ask our selves the following questions:
Interval Arithmetic opens up a whole new world of possibilities. Uncertainty in input data can be dealt with, round-off behaviour can be rigorously taken into account and even complete new algorithms can be designed that exploit the the properties of Interval Arithmetic to solve problems that have no other known solution. The SUN Fortran 95 and C++ compilers support this new paradigm in a language native way. Language support is provided for interval data types, basic arithmetic on intervals, interval extensions of standard intrinsic functions, relational operators, I/O, etc. In addition to existing intrinsic functions, many interval-specific intrinsic operators and functions are included. There is only one course topic: Interval Arithmetic. Bill Walster from Sun Microsystems will come over from the United States and give this course. He is not only the Interval Arithmetic expert within Sun, but also a very enthusiastic and talented presenter. But there is more. The organisation plans to have some guest speakers from DTU on the last day. They will talk about their use of Interval Arithmetic. As part of this addition to the training, Bill Walster will also share some of his research projects with us. The best way to learn Interval Arithmetic is to try it yourself. Therefore we have allocated a substantial amount of time to the labs and exercises. You will be working on specific problems to explore the possibilities of this fascinating technology. The programme is presented as follows:
There is no cost for the training itself but participants will be responsible for all other costs, like travel, hotel and meals. The training location is the Danish Technical University (DTU) in Lyngby (near Copenhagen) in Denmark - Building 305 - Lectures Room 053 - Labs Rooms 117 and 225. This training is open to all Sun customers, partners, employees and others interested. If you are interested in this exciting technology and want to learn more about it, please sign up for the training because space is limited. The registration deadline is July 28, 2002. Registration is very easy. Send an email to Anne Sorensen with the following information:
You will receive a confirmation of your registration request. Some pointers to more information on Interval Arithmetic:
Ruud van der Plas [News on Advanced IT] [Calendar] [Analysis] [IT in Medicine] |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |