Examples of the Usage of Infinities and Infinitesimals in Numerical Computations
暂无分享,去创建一个
[1] K. Gödel. Consistency of the Continuum Hypothesis. (AM-3) , 1940 .
[2] Louis D'Alotto,et al. Cellular automata using infinite computations , 2011, Appl. Math. Comput..
[3] Gabriele Lolli,et al. Infinitesimals and infinites in the history of mathematics: A brief survey , 2012, Appl. Math. Comput..
[4] Renato De Leone,et al. The use of grossone in Mathematical Programming and Operations Research , 2011, Appl. Math. Comput..
[5] Alfredo Garro,et al. Single-tape and multi-tape Turing machines through the lens of the Grossone methodology , 2013, The Journal of Supercomputing.
[6] P. Gordon. Numerical Cognition Without Words: Evidence from Amazonia , 2004, Science.
[7] J. M. Child. The Early Mathematical Manuscripts Of Leibniz , 1921, The Mathematical Gazette.
[8] Yaroslav D. Sergeyev,et al. Counting systems and the First Hilbert problem , 2010, 1203.4141.
[9] Alfredo Garro,et al. Observability of Turing Machines: A Refinement of the Theory of Computation , 2010, Informatica.
[10] Stephen P. Boyd,et al. Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.
[11] Yaroslav D. Sergeyev,et al. Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge ☆ , 2009, 1203.3150.
[12] Donald A. Martin,et al. Mathematical Problems. Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900 , 1979 .
[13] C. J. Keyser. Contributions to the Founding of the Theory of Transfinite Numbers , 1916 .
[14] Yaroslav D. Sergeyev,et al. Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer , 2013 .
[15] Yaroslav D. Sergeyev,et al. Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications , 2013 .
[16] A. Robinson. Non-standard analysis , 1966 .
[17] Massimo Veltri,et al. Usage of infinitesimals in the Menger's Sponge model of porosity , 2011, Appl. Math. Comput..
[18] M. Hayakawa,et al. Infinity Computations in Percolation Theory Applications , 2013 .
[19] R. Guy,et al. The Book of Numbers , 2019, The Crimean Karaim Bible.
[20] Yaroslav D. Sergeyev,et al. Higher order numerical differentiation on the Infinity Computer , 2011, Optim. Lett..
[21] M. Potter. Orders of infinity , 2004 .
[22] Yaroslav D. Sergeyev,et al. A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities , 2008, Informatica.
[23] Panos M. Pardalos,et al. Dynamics of Information Systems: Algorithmic Approaches , 2013 .
[24] Antanas Zilinskas,et al. On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions , 2011, Appl. Math. Comput..
[25] Gabriele Lolli,et al. Metamathematical investigations on the theory of Grossone , 2015, Appl. Math. Comput..
[26] Yaroslav D. Sergeyev,et al. Interpretation of percolation in terms of infinity computations , 2012, Appl. Math. Comput..
[27] Maurice Margenstern,et al. An application of Grossone to the study of a family of tilings of the hyperbolic plane , 2011, Appl. Math. Comput..
[28] Yaroslav D. Sergeyev,et al. Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers , 2007 .
[29] Elemer E Rosinger. Microscopes and Telescopes for Theoretical Physics: How Rich Locally and Large Globally is the Geometric Straight Line? , 2011 .
[30] Yaroslav D. Sergeyev,et al. Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains , 2009, 1203.4140.
[31] Yaroslav D. Sergeyev,et al. Numerical computations and mathematical modelling with infinite and infinitesimal numbers , 2012, ArXiv.
[32] Yaroslav D. Sergeyev,et al. On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function , 2011, 1203.4142.
[33] D. I. Iudin,et al. Infinity computations in cellular automaton forest-fire model , 2015, Commun. Nonlinear Sci. Numer. Simul..
[34] Yaroslav D. Sergeyev,et al. Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically , 2013, Appl. Math. Comput..
[35] Yaroslav D. Sergeyev. Using Blinking Fractals for Mathematical Modeling of Processes of Growth in Biological Systems , 2011, Informatica.
[36] Maurice Margenstern. Using grossone to count the number of elements of infinite sets and the connection with bijections , 2011, ArXiv.
[37] Anatoly A. Zhigljavsky,et al. Computing sums of conditionally convergent and divergent series using the concept of grossone , 2012, Appl. Math. Comput..