Linear Interpolation Calculator
Interpolated Value: -
Slope: -
Understanding Linear Interpolation
What is Linear Interpolation?
Linear interpolation is a method of estimating values between two known data points by fitting a straight line between them.
Key Formula
y = y₁ + (x - x₁)[(y₂ - y₁)/(x₂ - x₁)]
or
y = y₁ + (x - x₁)m
where m is the slope
Properties and Applications
Mathematical Properties
Linear function between points
First-order approximation
Preserves monotonicity
Continuous but not smooth
Error Analysis
Maximum error at midpoint
Error proportional to curvature
Second derivative bound
Error estimation methods
Applications
Data visualization
Computer graphics
Scientific computing
Digital signal processing
Advanced Topics
Extensions
Bilinear interpolation
Multivariate interpolation
Hermite interpolation
Shape-preserving methods
Alternative Methods
Polynomial interpolation
Spline interpolation
Rational interpolation
Trigonometric interpolation
Implementation
Numerical stability
Computational efficiency
Error handling
Optimization techniques