UID:
almahu_9947366135902882
Format:
1 online resource (297 p.)
ISBN:
1-282-29040-1
,
9786612290404
,
0-08-095545-2
Series Statement:
Mathematics in science and engineering ; 38
Content:
The theory of splines and their applications
Note:
Description based upon print version of record.
,
Front Cover; The Theory of Splines and Their Applications; Copyright Page; Contents; Preface; Chapter I. Introduction; 1.1. What Is a Spline?; 1.2. Recent Developments in the Theory of Splines; Chapter II. The Cubic Spline; 2.1. Introduction; 2.2. Existence, Uniqueness, and Best Approximation; 2.3. Convergence; 2.4. Equal Intervals; 2.5. Approximate Differentiation and Integration; 2.6. Curve Fitting; 2.7. Approximate Solution of Differential Equations; 2.8. Approximate Solution of Integral Equations; 2.9. Additional Existence and Convergence Theorems
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Chapter III. Intrinsic Properties of Cubic Splines3.1. The Minimum Norm Property; 3.2. The Best Approximation Property; 3.3. The Fundamental Identity; 3.4. The First Integral Relation; 3.5. Uniqueness; 3.6. Existence; 3.7. General Equations; 3.8. Convergence of Lower-Order Derivatives; 3.9. The Second Integral Relation; 3.10. Raising the Order of Convergence; 3.11. Convergence of Higher-Order Derivatives; 3.12. Limits on the Order of Convergence; 3.13. Hilbert Space Interpretation; 3.14. Convergence in Norm; 3.15. Canonical Mesh Bases and Their Properties; 3.16. Remainder Formulas
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3.17. Transformations Defined by a Mesh3.18. A Connection with Space Technology; Chapter IV. The Polynomial Spline; 4.1. Definition and Working Equations; 4.2. Equal Intervals; 4.3. Existence; 4.4. Convergence; 4.5. Quintic Splines of Deficiency 2, 3; 4.6. Convergence of Periodic Splines on Uniform Meshes; Chapter V. Intrinsic Properties of Polynomial Splines of Odd Degree; 5.1. Introduction; 5.2. The Fundamental Identity; 5.3. The First Integral Relation; 5.4. The Minimum Norm Property; 5.5. The Best Approximation Property; 5.6. Uniqueness; 5.7. Defining Equations; 5.8. Existence
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5.9. Convergence of Lower-Order Derivatives5.10. The Second Integral Relation; 5.11. Raising the Order of Convergence; 5.12. Convergence of Higher-Order Derivatives; 5.13. Limits on the Order of Convergence; 5.14. Hilbert Space Interpretation; 5.15. Convergence in Norm; 5.16. Canonical Mesh Bases and Their Properties; 5.17. Kernels and Integral Representations; 5.18. Representation and Approximation of Linear Functionals; Chapter VI. Generalized Splines; 6.1. Introduction; 6.2. The Fundamental Identity; 6.3. The First Integral Relation; 6.4. The Minimum Norm Property; 6.5. Uniqueness
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6.6. Defining Equations6.7. Existence; 6.8. Best Approximation; 6.9. Convergence of Lower-Order Derivatives; 6.10. The Second Integral Relation; 6.11. Raising the Order of Convergence; 6.12. Convergence of Higher-Order Derivatives; 6.13. Limits on the Order of Convergence; 6.14. Hilbert Space Interpretation; 6.15. Convergence in Norm; 6.16. Canonical Mesh Bases; 6.17. Kernels and Integral Representations; 6.18. Representation and Approximation of Linear Functionals; Chapter VII. The Doubly Cubic Spline; 7.1. Introduction; 7.2. Partial Splines
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7.3. Relation of Partial Splines to Doubly Cubic Splines
,
English
Additional Edition:
ISBN 0-12-044750-9
Language:
English
