Algebraic and Numerical Algorithms Algebraic computations refer to those performed exactly over some algebraic system. Such computations are used by students, scientists and engineers in manipulating formulae such as those found in calculus, linear algebra and differential equations. The first part of my research deals with developing, analyzing and implementing algorithms in this area. Indeed, such applications gave much initial impetus for the invention of computers.
Exact computations are inappropriate here because they are too slow.
Instead, arithmetic operations are replaced by approximate ones over the floating-point number system. Floating-point operations are fast, but each one results in a potential loss of accuracy. A good numerical algorithm is one which is fast and for which the loss of accuracy is understood and under control. The second part of my research deals with developing, analyzing and implementing numerical algorithms.