Conditional least squares polynomial approximation
نویسندگان
چکیده
منابع مشابه
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...
متن کاملThe Sensitivity of Least Squares Polynomial Approximation
Given integers N n 0, we consider the least squares problem of nding the vector of coeecients ~ P with respect to a polynomial basis P N j=0 wn(zj) 2 jf(zj) ? P (zj)j 2. Here a perturbation of the values f(zj) leads to some perturbation of the coeecient vector ~ P. We denote by n the maximal magniication of relative errors, i.e., the Euclidean condition number of the underlying weighted Vanderm...
متن کاملFast least-squares polynomial approximation in moving time windows
Only a few time series methods are applicable to signal trend analysis under real-time conditions. The use of orthogonal polynomials for least-squares approximations on discrete data turned out to be very e cient for providing estimators in the time domain. A polynomial extrapolation considering signal trends in a certain time window is obtainable even for high sampling rates. The presented met...
متن کاملLeast 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...
متن کاملFaster 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1964
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1964-0169361-1