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Finding serendipitous numerical patterns Edward Lorenz found the Lorenz attractor, an early example of a chaotic dynamical system, by investigating anomalous behaviours in a numerical weather model. The Ulam spiral was discovered by accident. The pattern in the Ulam numbers was discovered by accident.
Hilbert matrix — example of a matrix which is extremely ill-conditioned (and thus difficult to handle) Wilkinson matrix — example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues; Convergent matrix — square matrix whose successive powers approach the zero matrix; Algorithms for matrix multiplication:
A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity , numerical methods and computer algebra .
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
Predictive computational science is a scientific discipline concerned with the formulation, calibration, numerical solution, and validation of mathematical models designed to predict specific aspects of physical events, given initial and boundary conditions, and a set of characterizing parameters and associated uncertainties. [10]
Discovery science (also known as discovery-based science) is a scientific methodology which aims to find new patterns, correlations, and form hypotheses through the analysis of large-scale experimental data. The term “discovery science” encompasses various fields of study, including basic, translational, and computational science and ...
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Nowadays there are some 40 magazines about scientific modelling which offer all kinds of international forums. Since the 1960s there is a strongly growing number of books and magazines about specific forms of scientific modelling. There is also a lot of discussion about scientific modelling in the philosophy-of-science literature. A selection: