When some properties of a function are known, such as its regions of monotonicity, then a robust scalar root-finding algorithm such as reguli-falsi can be used, perhaps in conjunction with bracketed Newton interval steps. If nothing is known about the function, then the interval Newton method can be used to prove the monotonicity properties needed to get such a fast ``scalar'' method started.
The interval Newton technique requires a bound on the derivative of the function over an interval. For arbitrary functions, this can be accomplished with various interval arithmetics and automatic differentiation. For splines, tight derivative bounds can be found via control value differencing, subdivision, and the convex hull property.
In this talk I will present the Newton interval root-finding technique and discuss its properties and an implementation.
ICR/PAMI Joint Seminar ---------------------- ``On-Line Fingerprint Verification'' Anil K. Jain, Computer Science, Michigan State University 10:30 a.m.; DC1302 ICR SHORT COURSES: ------------------ ICR Members and Graduate Students supervised by ICR faculty members may attend free-of-charge subject to availability. Registration required: detailed info is available at the ICR Web site: http://icr.uwaterloo.ca September 16-17, 1997 ICR Short Course ``Software Engineering Practice: An Industry Perspective'' Jacob Slonim, Adjunct Professor, Computer Science, U. of Waterloo 9:30 a.m. - 4:30 p.m.; DC1304 Celebrity Lecture Series in Computer Science -------------------------------------------- Sponsored by the CSGSA SPEAKER: John Ousterhout Sun Microsystems Laboratories TITLE: ``Scripting: Higher Level Programming for the 21st Century.'' DATE: Wednesday, September 17, 1997 TIME: 1:30-2:30 p.m. ROOM: DC 1302 ABSTRACT As we near the end of the 20th century a fundamental change is occurring in the way people write computer programs. The change is a transition from system programming languages such as C or C++ to scripting languages such as Perl or Tcl. Although many people are participating in the change, few people realize that it is occurring and even fewer people know why it is happening. In this talk I will explain why scripting languages will handle many of the programming tasks of the next century better than system programming languages. Scripting languages represent a very different style of programming than system programming languages. They are designed for "gluing" applications, and use type less approaches to achieve a higher level of programming and more rapid application development. Increases in computer speed and changes in the application mix are making scripting languages more and more important for applications of the future.