conditioning of linear systems

SearchAdvancedHelp

(0.001 seconds)

1—10 of 12 matching pages

1: 3.2 Linear Algebra

… ►

§3.2(iii) Condition of Linear Systems

…

2: 32.4 Isomonodromy Problems

… ► ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ can be expressed as the compatibility condition of a linear system, called an isomonodromy problem or Lax pair. …

3: 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).

…

4: 3.11 Approximation Techniques

… ►With $b_0=1$, the last $q$ equations give $b_1,\mathrm{\dots },b_q$ as the solution of a system of linear equations. … ►(3.11.29) is a system of $n+1$ linear equations for the coefficients $a_0,a_1,\mathrm{\dots },a_n$. The matrix is symmetric and positive definite, but the system is ill-conditioned when $n$ is large because the lower rows of the matrix are approximately proportional to one another. … … ►Then the system (3.11.33) is diagonal and hence well-conditioned. …

5: 37.2 General Orthogonal Polynomials of Two Variables

… ►In the other direction, as an analogue of Favard’s theorem (see §18.2(viii) for the one-variable case), any polynomial system that satisfies the three-term relations (37.2.7), together with the conditions (37.2.10) and (37.2.8) of the coefficient matrices, must be orthonormal with respect to a positive definite linear functional. …

6: null

error generating summary

7: 3.6 Linear Difference Equations

§3.6 Linear Difference Equations

… ►Let us assume the normalizing condition is of the form $w_0=\lambda$, where $\lambda$ is a constant, and then solve the following tridiagonal system of algebraic equations for the unknowns $w_1^{(N)},w_2^{(N)},\mathrm{\dots },w_{N-1}^{(N)}$; see §3.2(ii). … ►

§3.6(vii) Linear Difference Equations of Other Orders

… ►or for systems of $k$ first-order inhomogeneous equations, boundary-value methods are the rule rather than the exception. Typically $k-\mathrm{\ell }$ conditions are prescribed at the beginning of the range, and $\mathrm{\ell }$ conditions at the end. …

8: Bibliography M

… ►

Some conjectures for root systems. SIAM J. Math. Anal. 13 (6), pp. 988–1007.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (S. Milne), ZentralBlatt

Referenced by:

§17.13, §17.14.

Encodings:

BibTeX

… ►

Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

ⓘ

External Links:

ISSN 1286-4889, FullText, MathReview, ZentralBlatt

Referenced by:

§18.37(iii).

Encodings:

BibTeX

… ►

ⓘ

Notes:

System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions, arbitrary precision integers, and arbitrary precision floating point numbers.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

… ►

Asymptotic analysis of edge-excited currents on a convex face of a perfectly conducting wedge under overlapping penumbra region conditions. IEEE Trans. Antennas and Propagation 44 (1), pp. 97–101.

ⓘ

External Links:

Document

Referenced by:

§9.14.

Encodings:

BibTeX

… ►

SciFace Software, Paderborn, Germany.

ⓘ

Notes:

Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

Referenced by:

§ ‣ Software Cross Index.

Encodings:

BibTeX

…

9: 3.8 Nonlinear Equations

… ►

Regula Falsi

… ►Inverse linear interpolation (§3.3(v)) is used to obtain the first approximation: … ►

§3.8(vi) Conditioning of Zeros

… ►are well separated but extremely ill-conditioned. … ►

§3.8(vii) Systems of Nonlinear Equations

…

10: 1.13 Differential Equations

… ►For extensions of these results to linear homogeneous differential equations of arbitrary order see Spigler (1984). … ►Assuming that $u(x)$ satisfies un-mixed boundary conditions of the form …or periodic boundary conditions … ►A regular Sturm-Liouville system will only have solutions for certain (real) values of $\lambda$, these are eigenvalues. … ►For a regular Sturm-Liouville system, equations (1.13.26) and (1.13.29) have: (i) identical eigenvalues, $\lambda$; (ii) the corresponding (real) eigenfunctions, $u(x)$ and $w(t)$, have the same number of zeros, also called nodes, for $t\in (0,c)$ as for $x\in (a,b)$; (iii) the eigenfunctions also satisfy the same type of boundary conditions, un-mixed or periodic, for both forms at the corresponding boundary points. …