Gram–Schmidt procedure

SearchAdvancedHelp

(0.001 seconds)

11—20 of 31 matching pages

11: 28.34 Methods of Computation

… ►

Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).

…

12: 6.18 Methods of Computation

… ►In addition, Acton (1974) developed a recurrence procedure, as follows. …

13: 30.7 Graphics

…

14: 28.32 Mathematical Applications

… ►See Schmidt and Wolf (1979). …

15: 31.9 Orthogonality

… ►For bi-orthogonal relations for path-multiplicative solutions see Schmidt (1979, §2.2). …

16: Bibliography S

… ►

Ein Verfahren zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung III. Numer. Math. 8 (1), pp. 68–71.

ⓘ

Notes:

Includes Algol program

External Links:

ISSN 0029-599X, Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§28.36(ii).

Encodings:

BibTeX

… ►

A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations. SIAM J. Math. Anal. 10 (4), pp. 823–838.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Ernest G. Kalnins), ZentralBlatt

Referenced by:

§28.32(i).

Encodings:

BibTeX

►

Die Lösung der linearen Differentialgleichung 2. Ordnung um zwei einfache Singularitäten durch Reihen nach hypergeometrischen Funktionen. J. Reine Angew. Math. 309, pp. 127–148.

ⓘ

External Links:

ISSN 0075-4102, MathReview (J. Nikolaus), ZentralBlatt

Referenced by:

§31.11(v), §31.6, §31.9(ii).

Encodings:

BibTeX

…

17: 19.36 Methods of Computation

… ►All cases of $R_F$, $R_C$, $R_J$, and $R_D$ are computed by essentially the same procedure (after transforming Cauchy principal values by means of (19.20.14) and (19.2.20)). … ►If $t_0=a_0$ and $\theta =-1$, so that $t_n=a_n$, then this procedure reduces to the AGM method for the complete integral. … ►A three-part computational procedure for $\mathrm{\Pi }(\varphi ,{\alpha }^2,k)$ is described by Franke (1965) for . …

18: 31.11 Expansions in Series of Hypergeometric Functions

… ►Schmidt (1979) gives expansions of path-multiplicative solutions (§31.6) in terms of doubly-infinite series of hypergeometric functions. …

19: 10.74 Methods of Computation

… ►If values of the Bessel functions $J_{\nu }\left(z\right)$, $Y_{\nu }\left(z\right)$, or the other functions treated in this chapter, are needed for integer-spaced ranges of values of the order $\nu$, then a simple and powerful procedure is provided by recurrence relations typified by the first of (10.6.1). …

20: 3.6 Linear Difference Equations

… ►However, there are alternative procedures that do not require $w_N$ and $w_{N+1}$ to be known in advance. … ►However, a more powerful procedure combines the solution of the algebraic equations with the determination of the optimum value of $N$. …