Understanding Interpolation Accuracy: Trade-offs Between Linear and Higher-Order Methods
By
nomemory
Pure flour-power. Hearty enough to carry you through lunch.
Summary
The article explores the mathematical and computational aspects of interpolation when working with tabulated function values. It discusses how linear interpolation is often sufficient but higher-order interpolation methods can provide more accurate results, though they may introduce increased numerical error. The content examines the trade-offs between interpolation error and numerical error, using examples of tabulated functions to illustrate the concepts. It references Richard Feynman's perspective on finding interest in seemingly mundane topics through deeper investigation.
Key quotes
· 5 pulledRichard Feynman said that almost everything becomes interesting if you look into it deeply enough.
Looking up numbers in a table is certainly not interesting, but it becomes more interesting when you dig into how well you can fill in the gaps.
If you want to know the value of a tabulated function between values of x given in the table, you have to use interpolation.
Linear interpolation is often adequate, but you could get more accurate results using higher-order interpolation.
When you interpolate a function from a table of values, higher order interpolation may reduce pure interpolation error while increasing numerical error.
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