Gram–Schmidt procedure

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1: 3.11 Approximation Techniques

… ►A more efficient procedure is as follows. … ►A general procedure is to approximate

F

by a rational function

R

(vanishing at infinity) and then approximate

f

r={\mathscr{L}}^{-1}R

. … ►A set of functions

\phi_{0}(x),\phi_{1}(x),\dots,\phi_{n}(x)

that is linearly independent on the set

x_{1},x_{2},\dots,x_{J}

(compare (3.11.36)) can always be orthogonalized in the sense given in the preceding paragraph by the Gram–Schmidt procedure; see Gautschi (1997a). …

2: Gerhard Wolf

… ► Schmidt) of the Chapter Double Confluent Heun Equation in the book Heun’s Differential Equations (A. …

3: Hans Volkmer

… ►Subsequently, he spent eleven years at the University of Essen as an assistant to Professor Dieter Schmidt, and then in 1990 joined the faculty at the University of Wisconsin–Milwaukee. …

4: 28.36 Software

… ►See also Clemm (1969), Delft Numerical Analysis Group (1973), Rengarajan and Lewis (1980), and Schäfke and Schmidt (1966). …

5: 17.18 Methods of Computation

… ►Method (1) can sometimes be improved by application of convergence acceleration procedures; see §3.9. …

6: 8.25 Methods of Computation

… ►A numerical inversion procedure is also given for calculating the value of

x

(with 10S accuracy), when

a

and

P\left(a,x\right)

are specified, based on Newton’s rule (§3.8(ii)). … ►An efficient procedure, based partly on the recurrence relations (8.8.5) and (8.8.6), is described in Gautschi (1979b, 1999). …

10: Bille C. Carlson

… ►In theoretical physics he is known for the “Carlson-Keller Orthogonalization”, published in 1957, Orthogonalization Procedures and the Localization of Wannier Functions, and the “Carlson-Keller Theorem”, published in 1961, Eigenvalues of Density Matrices. …