![]() ![]() The following Mathematica code utilizes a user defined procedure “Spline1” that creates the required piecewise linear function. Notice that for the procedure to work, the components of the data points have to satisfy. Repeating for the other coefficients, the required explicit equation has the form: For the first interval, the coefficients are: For each interval, a set of coefficients and are required for the linear interpolation. There are 11 data points surrounding 10 intervals. Find the explicit representation of the linear spline interpolating function for these data points. The linear function for each interval is defined using two coefficients, and therefore, we need to find coefficients. ![]() Given a set of data points, a piecewise linear (piecewise affine) spline can be defined as: Piecewise Linear Spline Interpolation Piecewise Linear (Piecewise Affine) Spline Interpolation Open Educational Resources Piecewise Interpolation: Derivatives Using Interpolation Functions.High-Accuracy Numerical Differentiation Formulas.Basic Numerical Differentiation Formulas.Linearization of Nonlinear Relationships.zy interp1 (x,y,z,'linear') Hereby one calculates the line between two adjacent points and gets zy by assuming that the point would be an element of those lines. ![]() Convergence of Jacobi and Gauss-Seidel Methods One way to find the y-values of z is piecewise linear interpolation.Cholesky Factorization for Positive Definite Symmetric Matrices. ![]()
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