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Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." "A spline is a function defined by polynomials in a piecewise manner."
The inverse of the Ackermann function appears in some time complexity results. For instance, the disjoint-set data structure takes amortized time per operation proportional to the inverse Ackermann function, [24] and cannot be made faster within the cell-probe model of computational complexity. [25]
In linear algebra and statistics, the partial inverse of a matrix is an operation related to Gaussian elimination which has applications in numerical analysis and statistics. It is also known by various authors as the principal pivot transform , or as the sweep , gyration , or exchange operator.
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point ; then is injective (or bijective onto the image) in a neighborhood of , the inverse is continuously differentiable near = (), and the derivative of the inverse function at is the reciprocal of the derivative of at : ′ = ′ = ′ (()).
Sliced inverse regression (SIR) is a tool for dimensionality reduction in the field of multivariate statistics. [ 1 ] In statistics , regression analysis is a method of studying the relationship between a response variable y and its input variable x _ {\displaystyle {\underline {x}}} , which is a p -dimensional vector.
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...
In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function. Lagrange inversion is a special case of the inverse function theorem.