65Dxx Numerical approximation and interpolation
This subtopic introduces the core ideas in numerical approximation and interpolation, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
65D05 Numerical interpolation
Overview
Numerical interpolation. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D07 Numerical computation using splines
Overview
Numerical computation using splines. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D10 Numerical smoothing, curve fitting
Overview
Numerical smoothing, curve fitting. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D12 Numerical integration of differential-algebraic equations
Overview
Numerical integration of differential-algebraic equations. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D15 Algorithms for approximation of functions
Overview
Algorithms for approximation of functions. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D17 Computer aided design (modeling of curves and surfaces)
Overview
Computer aided design (modeling of curves and surfaces). This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
Overview
Numerical aspects of computer graphics, image analysis, and computational geometry. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D19 Computational issues in computer and robotic vision
Overview
Computational issues in computer and robotic vision. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D20 Computation of special functions, construction of tables
Overview
Computation of special functions, construction of tables. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D25 Numerical differentiation
Overview
Numerical differentiation. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D30 Numerical integration
Overview
Numerical integration. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D32 Numerical quadrature and cubature formulas
Overview
Numerical quadrature and cubature formulas. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks
65D40 Numerical methods for trigonometric approximation and interpolation
Overview
Numerical methods for trigonometric approximation and interpolation. This topic studies numerical approximation and interpolation, including polynomial, spline, and functional approximation techniques.
Related Wikipedia Page
Numerical interpolation (Wikipedia)
Useful Links
Key Ideas
- approximation of functions and operators
- error estimates and stability
- adaptive interpolation and quadrature-related approximants
Typical Uses
Used to approximate complex functions and data with controllable accuracy in numerical workflows.
Applications
- Computer-aided design
- Scientific data fitting
- Numerical PDE and ODE preprocessing
References
Recommended Textbooks