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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