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AuthorSendov, B. author
TitleHausdorff Approximations [electronic resource] / by B. Sendov ; edited by Gerald Beer
ImprintDordrecht : Springer Netherlands, 1990
Connect tohttp://dx.doi.org/10.1007/978-94-009-0673-0
Descript 388 p. online resource

CONTENT

1 Elements of segment analysis -- ยง 1.1. Segment arithmetic -- ยง 1.2. Segment sequences -- ยง 1.3. Segment functions -- 2 Hausdorff distance -- ยง 2.1. Hausdorff distance between subsets of a metric space -- ยง 2.2. The metric space F? -- ยง 2.3. H-distancein A? and its properties -- ยง 2.4. Relationships between uniform distance and the Hausdorff distance -- ยง 2.5. The modulus of H-continuity -- ยง 2.6. The order of the modulus of H-continuity -- ยง 2.7. H-continuity on a subset -- ยง 2.8. H-distance with weight -- 3 Linear methods of approximation -- ยง 3.1. Convergence of sequences of positive operators -- ยง 3.2. The order of approximation of functions by positive linear operators -- ยง 3.3. Approximation of periodic functions by positive integral operators -- ยง 3.4. Approximation of functions by positive integral operators on a finite closed interval -- ยง 3.5. Approximation of functions by summation formulas on a finite closed interval -- ยง 3.6. Approximation of nonperiodic functions by integral operators on the entire real axis -- ยง 3.7. Convergence of derivatives of linear operators -- ยง 3.8. A-distance -- ยง 3.9. Approximation by partial sums of Fourier series -- 4 Best Hausdorff approximations -- ยง 4.1. Best approximation by algebraic and trigonometric polynomials -- ยง 4.2. Best approximation by rational functions -- ยง 4.3. Best approximation by spline functions -- ยง 4.4. Best approximation by piecewise monotone functions -- 5 Converse theorems -- ยง 5.1. Existence of a function with preassigned best approximations -- ยง 5.2. Converse theorems for the approximation by algebraic and trigonometric polynomials -- ยง 5.3. Converse theorems for approximation by spline functions -- ยง 5.4. Converse theorems for approximation by rational and partially monotone functions -- ยง 5.5. Converse theorems for approximation by positive linear operators -- 6 ?-Entropy, ?-capacity and widths -- ยง 6.1. ?-entropy and ?-capacity of the set F?M -- ยง 6.2. The number of (p,q)-corridors -- ยง 6.3. Labyrinths -- ยง 6.4. ?-entropy and ?-capacity of bounded sets of connected compact sets -- ยง 6.5. Widths -- 7 Approximation of curves and compact sets in the plane -- ยง 7.1. Approximation by polynomial curves -- ยง 7.2. Characterization of best approximation in terms of metric dimension -- ยง 7.3. Approximation by piecewise monotone curves -- ยง 7.4. Other methods for the approximation of curves in the plane -- 8 Numerical methods of best Hausdorff approximation -- ยง 8.1. One-sided Hausdorff distance -- ยง 8.2. Coincidence of polynomials of best approximation with respect to one- and two-sided Hausdorff distance -- ยง 8.3. Numerical methods for calculating the polynomial of best one-sided approximation -- References -- Author Index -- Notation Index


Mathematics Approximation theory System theory Computer mathematics Electrical engineering Mathematics Approximations and Expansions Computational Mathematics and Numerical Analysis Electrical Engineering Systems Theory Control



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