Interval Arithmetic Training For Beginners
The Danish Technical University
August 26-28, 2002
With great pleasure we announce this unique training on Interval Arithmetic. 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.
What Is An Interval ?
An interval is a range of numbers bounded by the interval's endpoints.
What Is Interval Arithmetic ?
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 reexamined.
Why Is Interval Arithmetic Needed ?
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:
Intervals create a tight logical connection between computing and scientific, engineering, and mathematical reality. As a consequence, it becomes possible to:
Computing speed produces unprecedented opportunities and risks. Unfortunately, without intervals, the opportunities cannot be exploited and the risks cannot be avoided.
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:
Compute correct results the first time. Guarantee the accuracy of computed results. Validate computed problem solutions without benefit of independent verification. Compute answers to new questions that have never before been asked or answered.
|"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:
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.
If you are interested in this exciting technology and want to learn more about it, sign up for the training ! Do it now, space is limited !
Some pointers to more information on Interval Arithmetic:
The Sun web site:
Other links to more information, which are also available as links in the second URL, above are:
Other than basic programming skills in Fortran (or other languages, such as Pascal, C, C++, and/or Java) and an interest in this topic, no specific prerequisites are required. The training targets the absolute beginners in Interval Arithmetic. We will build everything up from scratch using Fortran. All aspects of intervals will be covered during the course. Last, but certainly not least, you will also be able to ask any questions you ever wanted to ask about this topic.
There is only topic: Interval Arithmetic.
We are delighted to have Bill Walster from Sun Microsystems to come over from the US 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. We plan 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 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.
Monday August 26, 2002
|Topic||Start time||End time|
|Training - Part I||9:30||10:45|
|Training - Part II||11:00||12:00|
|Training - Part III||14:15||15:15|
|Training - Part IV||15:30||17:00|
Tuesday August 27, 2002
|Topic||Start time||End time|
|Training - Part V||9:00||10:30|
|Training - Part VI||13:00||14:30|
|Training - Part VII||14:45||15:45|
Wednesday August 28, 2002
|Topic||Start time||End time|
|Training - Part VIII||9:00||10:30|
Cost of the training
We will not charge for the training itself. You will be responsible for all other costs, like travel, hotel and meals.
The Danish Technical University (DTU)
Lyngby (near Copenhagen)
|Labs||Rooms 117 and 225|
The URL of the DTU web site (also in English) is: http://www.dtu.dk
On this web site you will find campus maps.
This training is open to all Sun customers, partners, employees and others interested.
Registration is very easy. Send an email to Anne Sorensen (email@example.com) with the following information:
The registration deadline is July 28, 2002. Seating is limited and we recommend to register as early as possible ! Allocation is on a first come, first serve basis. If demand exceeds our capacity, we may have to restrict attendance to 2-3 persons per company/institute.
Note: if you cancel your registration after August 19, we may have to charge you a cancellation fee.
You are most welcome to stay wherever you like.
One site with hotel information is: http://www.copenhagen-hotels.dk/index.asp
For those interested to stay in a nearby location, we have reserved a block of rooms at the following hotel:
Vedbaek Strandvej 391
Phone +45 45891711
Fax +45 45891722
You can find more information on this hotel through the above given website. In the "Search by city" field select "Vedbaek" and you'll get a link to the Marina Hotel.
The price per night is DKr. 875 (approximately 120 Euro). Breakfast is included.
On the training days we will arrange a shuttle bus between the hotel and the training location. This bus will leave at a fixed time in the morning and at the end of the training day. All other transportation is at your own expense.
There is no specific dress code. Please wear whatever you feel comfortable in.
Somewhat unpredictable at this time of the year, but typically the temperature
is around 20-25 deg. C. Be prepared for cooler weather and/or rain though.