Mathematics - iii (Differential Calculus) - Vol 4 | 2. Interpolation Formulas by Abraham | Learn Smarter
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2. Interpolation Formulas

Interpolation is an essential method used to estimate values within a range defined by known data points. The chapter outlines various classical interpolation formulas including Newton's, Lagrange's, and Gregory-Newton methods. Each method is tailored to specific data distributions and conditions, providing insights on their applicability, efficiency, and limitations. Understanding the differences among these interpolation techniques aids in selecting the appropriate method for various numerical analysis situations.

Sections

  • 2

    Interpolation & Numerical Methods

    This section provides an overview of interpolation methods used to estimate unknown values from known data points, focusing on classical formulas such as Newton's, Lagrange's, and Gregory-Newton methods.

    Learning Practice

  • 2.1

    Interpolation Basics

    Interpolation is a method used to estimate unknown values between known data points within a dataset.

    Learning Practice

  • 2.2

    Finite Differences

    Finite differences are a foundational concept in interpolation, providing a means of estimating values of functions based on differences at discrete points.

    Learning Practice

  • 2.3

    Newton’s Forward Interpolation Formula

    Newton’s Forward Interpolation Formula is used to estimate the value of a function near the beginning of a dataset with equally spaced data points.

    Learning Practice

  • 2.4

    Newton’s Backward Interpolation Formula

    Newton's Backward Interpolation Formula is used to estimate values when the interpolation point is near the end of a dataset.

    Learning Practice

  • 2.5

    Central Difference Interpolation Formulas

    Central Difference Interpolation Formulas use surrounding data points for estimating function values, important for numerical methods.

    Learning Practice

  • 2.6

    Lagrange’s Interpolation Formula

    Lagrange’s Interpolation Formula provides a method to estimate values of a function for unequally spaced data points.

    Learning Practice

  • 2.7

    Newton’s Divided Difference Formula

    Newton's Divided Difference Formula is a method for polynomial interpolation based on unequally spaced data points.

    Learning Practice

  • 2.8

    Error In Interpolation

    This section discusses the error in interpolation methods, emphasizing the general error term in the Newton form.

    Learning Practice

  • 2.9

    Comparison Of Interpolation Methods

    This section compares various interpolation methods, highlighting their use cases, spacing requirements, and efficiency.

    Learning Practice

References

unit 4 ch2.pdf

Class Notes

Memorization

What we have learnt

  • Interpolation estimates unk...
  • Newton's interpolation form...
  • Different interpolation met...

Final Test

Revision Tests