Approximation of Least Squares Regression on Nested Subspaces

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...

Penalized Least Squares Regression: Fast Computation via EÆ ient Approximation

Least Squares Approximation

In many applications we want to find an approximation for a function, for example for differential equations. Example problem: We want to understand how a calculator or computer can evaluate sinx for a given value x. The processor can essentially only perform addition, multiplication, division. Therefore we can try to approximate the function with a polynomial. We use the notation Pn for polyno...

Least-squares polynomial approximation

We construct symmetric polar WAMs (Weakly Admissible Meshes) with low cardinality for least-squares polynomial approximation on the disk. These are then mapped to an arbitrary triangle. Numerical tests show that the growth of the least-squares projection uniform norm is much slower than the theoretical bound, and even slower than that of the Lebesgue constant of the best known interpolation poi...

Faster Least Squares Approximation

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n d. Then, existing exact methods find a solution vector in O(nd2) time. We present two randomized algorithms that provide accurate relative-error approximations...