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Lecture
Spline Interpolation: Definition and Error Analysis
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Image Processing II: B-spline Properties and Gradient Operators
Explores B-spline properties, gradient operators, interpolation, and differentiation filters in image processing.
Splines: Fundamentals and Applications
Explores B-splines, natural cubic splines, and smoothing splines in regression problems and their practical applications.
Gauss-Legendre Quadrature Formulas
Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.
Image Processing II: Polynomial Splines
Explores spatial transformations, polynomial splines, B-spline properties, interpolation, and differential operators in image processing.
Trigonometric Interpolation: Approximation of Periodic Functions and Signals
Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.
Piecewise Polynomial Interpolation: Splines
Covers piecewise polynomial interpolation with splines, focusing on Lagrange interpolation with Chebyshev nodes and error convergence.
Approximation of Data
Covers the least squares method for approximating data and handling errors.
Numerical Differentiation: Finite Differences
Explores numerical differentiation using finite differences and addresses the impact of errors in computer computations.