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Mahāvīra (or Mahaviracharya, "Mahavira the Teacher") was a 9th-century Indian Jain mathematician possibly born in Mysore, in India. [1] [2] [3] He authored Gaṇita-sāra-saṅgraha (Ganita Sara Sangraha) or the Compendium on the gist of Mathematics in 850 CE. [4] He was patronised by the Rashtrakuta emperor Amoghavarsha. [4]
Rangachar Narayana Iyengar (born 2 June 1943), also known as RNI, is a civil engineer and professor from India. He was with the Indian Institute of Science , Bangalore for about four decades. He has been the director of Central Building Research Institute, Roorkee (1994–2000).
Necessary conditions for a numerical method to effectively approximate (,) = are that and that behaves like when . So, a numerical method is called consistent if and only if the sequence of functions { F n } n ∈ N {\displaystyle \left\{F_{n}\right\}_{n\in \mathbb {N} }} pointwise converges to F {\displaystyle F} on the set S {\displaystyle S ...
multiderivative methods, which use not only the function f but also its derivatives. This class includes Hermite–Obreschkoff methods and Fehlberg methods, as well as methods like the Parker–Sochacki method [17] or Bychkov–Scherbakov method, which compute the coefficients of the Taylor series of the solution y recursively.
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [19]Probabilistic numerics have also been studied for mathematical optimization, which consist of finding the minimum or maximum of some objective function given (possibly noisy or indirect) evaluations of that function at a set of points.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control , [ 1 ] and can be formulated to construct solutions in a memory-efficient, factored form.