Mathematical Bivariate Polynomial Matrix Fitting for Thermal Drift Compensation
Bivariate polynomial matrix fitting corrects non-linear sensor thermal drift when inputs are normalized and solved via singular value decomposition.
Chebyshev Nodes
Interpolation Points
Numerical analysis employs chebyshev nodes to minimize the phenomenon of runge oscillation during polynomial approximation. These points represent the roots of the first kind chebyshev polynomial defined on the interval of negative one to one. Optimal distribution of these coordinates clusters the observations toward the boundaries of the domain.
This arrangement suppresses the large errors that occur near the edges when using equidistant sampling.
Distribution Geometry
Mapping these nodes requires mapping the cosine function across a set of points spaced uniformly in an angular space. Calculating each location involves taking the cosine of the product of a specific fraction and pi. Transformations to an arbitrary interval require a linear shift and scaling of the normalized coordinates.
Stability remains the primary advantage of this spacing because it forces the maximum difference between the function and its interpolant to decrease as the number of nodes increases.
Error Control
Spectral methods rely on this specific placement to ensure high order convergence for analytic functions. Precise alignment reduces the influence of noise within the underlying data set. Calibration of digital filters often utilizes this node structure to maintain a flat frequency response across the passband.
Sensitivity to rounding error remains lower here than with standard polynomial fitting methods because the weights of the associated quadrature rule remain positive.
Metrological Limits
Verification of approximation accuracy depends on the regularity of the sampled signal. Discontinuities within the data force the error to remain large even with an ideal node selection. Sampling density must exceed the highest frequency component to prevent aliasing effects from distorting the results.
Proper selection of node count defines the resolution of the final model.