Chebyshev interpolant and its distance from the min-max polynomial

Economization

Additional reading:

• M. J. D. Powell, On the maximum errors of polynomial approximations
defined by interpolation and by least squares criteria,
Computer J., 1967, vol. 9, pp. 404-407,
[pdf file]

K. Atkinson, An INTRODUCTION to NUMERICAL ANALYSIS, Wiley, 1987

S. Conte & C. deBoor, ELEMENTARY NUMERICAL ANALYSIS, McGraw-Hill User friendly; Shows how 'it' works; Proofs, exercises and notes

G. Dahlquist & A. Bjorck, NUMERICAL METHODS, Prentice-Hall, User friendly; Shows how 'it' works; Exercises

E. Isaacson & H. Keller, ANALYSIS of NUMERICAL METHODS, Wiley The 'First'; Proofs; out-dated in certain aspects; Encrypted
message in Preface

A. Ralston & P. Rabinowitz, FIRST COURSE in
NUMERICAL ANALYSIS, 2nd ed., McGraw-hill, Detailed; Scholarly written; Comprehensive; Proofs exercises and notes

J. Stoer & R. Bulrisch, INTRODUCTION TO NUMERICAL ANALYSIS, 2nd ed., Springer detailed account on approximation, linear solvers & eigen-solvers,
ODE solvers,..

B. Wendroff, THEORETICAL NUMERICAL ANALYSIS, Academic Press, 1966 Only the 'Proofs'; elegant presentation

APPROXIMATION THEORY

E. W. Cheney, INTRODUCTION TO APPROXIMATION THEORY Classical

P. Davis, INTERPOLATION & APPROXIMATION, Dover Very readable

T. Rivlin, AN INTRODUCTION to the APPROXIMATION of FUNCTIONS Classical

R. DeVore & G. Lorentz, CONSTRUCTIVE APPROXIMATION, Springer A detailed account from classical theory to the modern theory; everything; Proofs exercises and notes

NUMERICAL INTEGRATION

F. Davis & P. Rabinowitz, NUMERICAL INTEGRATION, Everything...

(mainly) ITERATIVE SOLUTION OF LINEAR SYSTEMS

A. Householder, THE THEORY OF MATRICES IN NUMERICAL ANALYSIS The theoretical part by one of
the grand masters; Outdated in some aspects

G. H. Golub & Van Loan, MATRIX COMPUTATIONS, The basic modern reference