Blar i Bergen Open Research Archive på forfatter "Steihaug, Trond"
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Approximating cube roots of integers, after Heron’s Metrica III.20
Steihaug, Trond; Rogers, D. G. (Peer reviewed; Journal article, 2013) -
Computational Science in the 17th Century. Numerical Solution of Algebraic Equations: Digit–by–Digit Computation
Steihaug, Trond (Chapter, 2022)In this paper we give a complete overview of test–problems by Viète from 1600, Harriot from 1631 and Oughtred from 1647. The original material is not easily accessible due to archaic language and lack of conciseness. Viéte’s ... -
Computational science in the eighteenth century. Test cases for the methods of Newton, Raphson, and Halley: 1685 to 1745
Steihaug, Trond (Peer reviewed; Journal article, 2020)This is an overview of examples and problems posed in the late 1600s up to the mid 1700s for the purpose of testing or explaining the two different implementations of the Newton-Raphson method, Newton’s method as described ... -
Generating a synthetic diffusion tensor dataset
Bergmann, Ørjan; Lundervold, Arvid; Steihaug, Trond (Peer reviewed; Journal article, 2005)During the last years, many techniques for de-noising, segmentation and fiber-tracking have been applied to diffusion tensor MR image data (DTI) from human and animal brains. However, evaluating such methods may be difficult ... -
A minimum requiring angle trisection
Steihaug, Trond; Rogers, D. G. (Peer reviewed; Journal article, 2009) -
A New Generating Set Search Algorithm for Partially Separable Functions
Frimannslund, Lennart; Steihaug, Trond (Chapter; Peer reviewed, 2010)A new derivative-free optimization method for unconstrained optimization of partially separable functions is presented. Using average curvature information computed from sampled function values the method generates an ... -
On a New Method for Derivative Free Optimization
Frimannslund, Lennart; Steihaug, Trond (Peer reviewed; Journal article, 2011)A new derivative-free optimization method for unconstrained optimization of partially separable functions is presented. Using average curvature information computed from sampled function values the method generates an ... -
On the Square Root Computation in Liber Abaci and De Practica Geometrie by Fibonacci
Steihaug, Trond (Journal article; Peer reviewed, 2024)We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the ... -
A polynomial-time algorithm for LO based on generalized logarithmic barrier functions
El Ghami, Mohamed; Ivanov, I.D.; Roos, C.; Steihaug, Trond (Peer reviewed; Journal article, 2008) -
A Story of Computational Science: Colonel Titus’ Problem from the 17th Century
Steihaug, Trond (Journal article, 2022-06-14)Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow a single test example over more than 250 years. In 1685, John Wallis published A treatise of algebra, both historical ...