Chapter 5: Derivatives and Integration
نویسنده
چکیده
2 Numerical and Symbolic Integration 2 2.1 Cubature Formulae Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Constructing Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Interpolatory Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Ideal Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.3 Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.4 The characterization of minimal formulae and the reproducing kernel . . . . . 5 2.3 Gauss Formula on an A-patch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Gauss Points and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.2 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 T-method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 S-method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
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