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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.
When one does not know the exact solution, one may look for the approximation with small residual. Residuals appear in many areas in mathematics, including iterative solvers such as the generalized minimal residual method, which seeks solutions to equations by systematically minimizing the residual.
Modal analysis using FEM — solution of eigenvalue problems to find natural vibrations; Céa's lemma — solution in the finite-element space is an almost best approximation in that space of the true solution; Patch test (finite elements) — simple test for the quality of a finite element
P. Padé approximant; Padé table; Pairwise summation; Parareal; Partial differential algebraic equation; Particle method; Peano kernel theorem; Piecewise linear continuation
Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic-matrix-and-graph theory. Other areas of computational mathematics include computer algebra and symbolic computation .
(Extensive online material on ODE numerical analysis history, for English-language material on the history of ODE numerical analysis, see, for example, the paper books by Chabert and Goldstine quoted by him.) Pchelintsev, A.N. (2020). "An accurate numerical method and algorithm for constructing solutions of chaotic systems".