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  2. Linear interpolation - Wikipedia

    en.wikipedia.org/wiki/Linear_interpolation

    Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

  3. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    e. In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter, usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree, can't be integrated directly.

  4. Kronecker product - Wikipedia

    en.wikipedia.org/wiki/Kronecker_product

    Kronecker product. In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a ...

  5. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    Nonstandard analysis. v. t. e. In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.

  6. Vector-valued function - Wikipedia

    en.wikipedia.org/wiki/Vector-valued_function

    Vector-valued function. A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or ...

  7. State-space representation - Wikipedia

    en.wikipedia.org/wiki/State-space_representation

    State-space representation. In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations. Such variables, called state variables, evolve over time in a way that ...

  8. Spline (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Spline_(mathematics)

    A vector r = (r 1, …, r k–1) such that the spline has smoothness at t i for i = 1, …, k – 1 is called a smoothness vector for the spline. Given a knot vector t, a degree n, and a smoothness vector r for t, one can consider the set of all splines of degree ≤ n having knot vector t and smoothness vector r. Equipped with the operation of ...

  9. Cross product - Wikipedia

    en.wikipedia.org/wiki/Cross_product

    In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b ...

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