Step-by-step Newton forward/backward, divided difference & Lagrange interpolation with full tables.
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System of Linear Equations: Solve linear systems with RREF, Gauss-Jacobi, and Gauss-Seidel methods using full step-by-step tables.
Open tool| i | xᵢ | yᵢ or f(xᵢ) | Action |
|---|---|---|---|
| 0 | |||
| 1 | |||
| 2 | |||
| 3 |
| i | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| xᵢ | 20 | 23 | 26 | 29 |
| yᵢ | 0.342 | 0.3907 | 0.4384 | 0.4848 |
Newton's Forward Interpolation. x = 21 is nearer the beginning of the table, so Newton's Forward formula is used.
| x | y | Δ | Δ² | Δ³ |
|---|---|---|---|---|
20 | 0.342 | |||
0.0487 Δy₀ = y₁ − y₀ = 0.3907 − 0.342 = 0.0487 | ||||
23 | 0.3907 | -0.001 Δ²y₀ = Δy₁ − Δy₀ = 0.0477 − 0.0487 = -0.001 | ||
0.0477 Δy₁ = y₂ − y₁ = 0.4384 − 0.3907 = 0.0477 | -0.0003 Δ³y₀ = Δ²y₁ − Δ²y₀ = -0.0013 − -0.001 = -0.0003 | |||
26 | 0.4384 | -0.0013 Δ²y₁ = Δy₂ − Δy₁ = 0.0464 − 0.0477 = -0.0013 | ||
0.0464 Δy₂ = y₃ − y₂ = 0.4848 − 0.4384 = 0.0464 | ||||
29 | 0.4848 |
Highlighted cells are the diagonal used in the formula.
h = 3 (common difference of x-values).
