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.
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What we have learnt
- Interpolation estimates unknown values between known data points.
- Newton's interpolation formulas are effective for equally spaced data, while Lagrange's formula is suited for unequally spaced data.
- Different interpolation methods have varying levels of complexity and accuracy depending on the specific use case.
Key Concepts
- -- Interpolation
- The process of estimating unknown values within a range defined by known data points.
- -- Newton’s Forward Interpolation Formula
- Used when the value of x is near the beginning of the dataset with equally spaced points.
- -- Lagrange’s Interpolation Formula
- A formula to estimate values for unequally spaced data points using polynomial interpolation.
- -- Finite Differences
- A technique involving the calculation of differences between data points, forming the basis for interpolation formulas.
- -- Central Difference
- An interpolation method that utilizes values around the point of interpolation to improve accuracy.
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