The theory of uniform approximation I. Non-asymptotic theoretical problems
S. Paszkowski
GDML_Books, (1962), p.

CONTENTSIntroduction..................................................................................................................................................................................... 3CHAPTER I. Basic properties of the best polynomials1. Existence, uniqueness and the characteristic properties of the best polynomials............................................................................... 62. The direct application of the theorem concerning the (n, F)-points to computing the best polynomials. The Chebyshev polynomials....... 153. The characteristic properties of pairs of successive best polynomials........................................................................................................................... 26CHAPTER II. Estimation of error of the beet approximation4. Basic theorems................................................................................................................................................................................................. 335. Vallée Poussin type estimations................................................................... 386. Estimation of the error of the best approximation for functions which are differentiable several times........................................ 537. Estimation of the (n + 1)-st error of the best approximation based upon the knowledge of the n-th best polynomial................... 578. The relation between the error of the best approximation and the interval of approximation.................................................. 65CHAPTER III. The distribution of (n)-points in the interval of approximation9. The estimates dependent upon the value of the ratio εn+1(ξ)εn(ξ)....................................................................................... 7010. Auxiliary theorems..................................................................... 8411. The estimates dependent upon the properties of the derivatives of the function ξ. General theorems....................................... 9212. The estimates dependent upon the properties of the derivatives of the function ξ. The choice of function γp............................. 111CHAPTER IV. Methods of computing well-approximating and best polynomials13. Well-approximating polynomials................................................................................................................................................................ 12114. Approximation of families of functions. The Zolotarev polynomials................................................................................................. 14015. The theory of the method of Remez................................................................................................................................................... 15616. Other methods of computing the best polynomials................................................................................................................................ 169References..................................................................................................................................................... 175

EUDML-ID : urn:eudml:doc:268542 
@book{bwmeta1.element.zamlynska-37f8ba75-b173-4bd0-b954-34335052b067,
     author = {S. Paszkowski},
     title = {The theory of uniform approximation I. Non-asymptotic theoretical problems},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1962},
     zbl = {0101.28802},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-37f8ba75-b173-4bd0-b954-34335052b067}
}

S. Paszkowski. The theory of uniform approximation I. Non-asymptotic theoretical problems. GDML_Books (1962),  http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-37f8ba75-b173-4bd0-b954-34335052b067/