In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots). In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher degrees.
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Lagrange polynomial
In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points and numbers, the Lagrange polynomial is the polynomial of the least degree that at each point assumes the corresponding value (i.e. the functions coincide at each point).
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e.
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Fortran
Fortran (previously FORTRAN) is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them.
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