A Story of Computational Science: Colonel Titus’ Problem from the 17th Century

Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow single test example over more than 250 years. 1685, John Wallis published A treatise algebra, both historical practical, containing solution Colonel Titus’ problem that was proposed to him around 1650. The Titus consists three algebraic quadratic equations unknowns, which transformed into finding roots fourth-order (quartic) polynomial. When Joseph Raphson his method 1690, he demonstrated on 32 one examples quartic equation. Edmund Halley later used same polynomial as an for new methods 1694. Although Vietè, is digit–by–digit method, efficient are clearly works by Halley. For years equation has been wide range nonlinear equations. This provides overview first derived Wallis. four positive found be very useful analyzing number intervals individual roots, Cardan–Ferrari direct approach solving equations, Sturm’s determining real equation, together with two other likely set compare different iteration