Iterative Solution of Large Linear SystemsCourier Corporation, 2003. 1. 1. - 570페이지 The frontier between 'law' and 'politics' is not always clear-cut. A large area exists where courts operate, but where governments and parliaments also make decisions. Tim Koopmans compares the way American, British, French and German law and politics deal with different issues: in many instances subjects which are highly 'political' in one country constitute legal issues in another. Is there, for example a 'sovereign Parliament' (as there is in Britain), or will courts control the compatibility of statutes with the Constitution (as in the United States and Germany)? How far can courts go in controlling the legality of administrative action? Are there general legal theories about the frontier between what courts and what politics can do? Koopmans considers case law on a range of issues, including human rights protection, federalism, separation of powers, equal protection and the impact of European and international law. |
목차
INTRODUCTION | 1 |
MATRIX PRELIMINARIES | 7 |
LINEAR STATIONARY ITERATIVE METHODS | 63 |
CONVERGENCE OF THE BASIC ITERATIVE METHODS | 106 |
EIGENVALUES OF THE SOR METHOD FOR CONSISTENTLY ORDERED MATRICES | 140 |
DETERMINATION OF THE OPTIMUM RELAXATION FACTOR | 169 |
NORMS OF THE SOR METHOD | 233 |
THE MODIFIED SOR METHOD FIXED PARAMETERS | 271 |
SEMIITERATIVE METHODS | 344 |
EXTENSIONS OF THE SOR THEORY STIELTJES MATRICES | 391 |
GENERALIZED CONSISTENTLY ORDERED MATRICES | 404 |
GROUP ITERATIVE METHODS | 434 |
SYMMETRIC SOR METHOD AND RELATED METHODS | 461 |
SECONDDEGREE METHODS | 486 |
ALTERNATING DIRECTION IMPLICIT METHODS | 495 |
SELECTION OF ITERATIVE METHOD | 553 |
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A₁ CCSI method Chapter CO(q columns compatible ordering vector completely consistent completes the proof compute consider consistently ordered matrix corresponding defined determine diag diagonal matrix difference equation differential equation Dirichlet problem eigenvalues eigenvectors Evidently exists function Gauss-Seidel method given GS method GS-SI method GS-SSI Hence holds i₁ integers irreducible iterative method J-SI Jordan canonical form L-matrix Lemma linear system matrix norm mesh points method converges model problem Moreover MSOR nonnegative nonsingular matrix nonvanishing diagonal elements number of iterations obtain permutation matrix polynomial positive definite matrix positive diagonal elements proof of Theorem Property Aq r)-matrix R₁ R₂ rate of convergence relaxation factor S₁ S₂ satisfies Section semi-iterative method solution solving SOR method spectral radius SSOR SUPPLEMENTARY DISCUSSION symmetric Theorem 2.1 vanish Varga Verify w₁ Wachspress weak diagonal dominance zero μ² ω₁ ωμ ωω