QR Decomposition Least Squares Calculator

Numerically solve least squares using orthogonal-triangular factorization for stability and accuracy today. Input matrix A and observation vector b; validate dimensions automatically for reliability. Compute Q and R, then solve Rx = Qᵀb by back substitution. Inspect residuals, condition estimates, and step-by-step numeric workings for insight. Export tables and solutions as CSV and PDF.

Matrix A (m×n) — rows on new lines, values comma or space separated

Vector b (length m) — one value per line

Ridge λ (scalar ≥ 0)

Ignored if auto-λ is on or λ_j provided.

Per-column λ_j (length n, optional)

Regularization basis

If using λ_j, choose whether penalties apply to x or z.

Auto-select scalar λ with L-curve

λ min

λ max

Grid points

Scale columns of A to unit 2-norm

Use weighted least squares (vector w)

Weights w (length m) — optional

Use covariance Σ (m×m SPD)

Covariance Σ (rows newline, values comma/space separated)

If provided, Σ overrides weights. We prewhiten using Cholesky.

Decimal places

Size cap (m×n)

Enable column pivoting (recommended)

Override size cap

Tip: A should have at least as many rows as columns (m ≥ n).

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