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1. A chronological and mathematical overview of digital circle generation algorithms

Barrera, Tony

et al.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

Hast, Anders

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

Bengtsson, Ewert

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

Circles are one of the basic drawing primitives for computers and while the naive way of setting up an equation for drawing circles is simple, implementing it in an efficient way using integer arithmetic has resulted in quite a few different algorithms. We present a short chronological overview of the most important publications of such digital circle generation algorithms. Bresenham is often assumed to have invented the first all integer circle algorithm. However, there were other algorithms published before his first official publication, which did not use floating point operations. Furthermore, we present both a 4- and an 8-connected all integer algorithm. Both of them proceed without any multiplication, using just one addition per iteration to compute the decision variable, which makes them more efficient than previously published algorithms.

The justification and rationale for analytically continuing quantum mechanics into the complex plane are recognized and briefly discussed. This extension is described by a complex symmetric representation, which is derived and demonstrated to include general Jordan block forms of Segre characteristics larger than one. Various applications in physics and chemistry, in which this extension appears necessary, are pointed out.

3. Generalized Newton multi-step iterative methods GMN<sub><em>p,m</em></sub> for solving systems of nonlinear equationsKouser, Salima

et al.

Ur Rehman, Shafiq

Ahmad, Fayyaz

Serra-Capizzano, Stefano

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

4. Sampling formula for convolution with a prolateLevitina, T.

et al.

Brändas, Erkki J.

Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.

Sampling formula for convolution with a prolate2008In: International Journal of Computer Mathematics, ISSN 0020-7160, E-ISSN 1029-0265, Vol. 85, no 3-4, p. 487-496Article in journal (Refereed)

Abstract [en]

Eigenfunctions of the Finite Fourier Transform, often referred to as 'prolates', are band-limited and highly concentrated at a finite time-interval. Both features are acquired by the convolution of a band-limited function with a prolate. This permits interpolation of such a convolution by the Walter and Shen sampling formula in terms of prolates, although the Fourier transform of the convolution is not necessarily even continuous and the concentration interval is twice as large as that of a prolate. Rigorous error estimates are given as dependent on the truncation limits. The accuracy achieved is tested by numerical examples.

5. A highly accurate adaptive finite difference solver for the Black–Scholes equationLinde, Gunilla

et al.

Persson, Jonas

von Sydow, Lina

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

6. BENCHOP—The BENCHmarking project in Option Pricing

von Sydow, Lina

et al.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Höök, Lars Josef

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Larsson, Elisabeth

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Lindström, Erik

Milovanović, Slobodan

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Persson, Jonas

Shcherbakov, Victor

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Milovanović, Slobodan

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.

Larsson, Elisabeth

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.

8. Adaptive finite differences and IMEX time-stepping to price options under Bates model

von Sydow, Lina

et al.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.