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Brent Method Calculator

Brent’s method (golden section plus inverse parabolic interpolation) for a minimum of a polynomial, sin, or exp on [a, b]. Same engine as One-Dimensional Optimization. Not root-finding Brent. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 11/11 tests · Production surface contract 2/2 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
xmin and fmin of poly, sin, or exp on [a, b] by Brent’s 1-D minimizer.
Scope
Minimize only
Verification
Engine tested · 11/11 tests · Production surface contract 2/2 · Specification checked · v1.0.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
3 golden · 2 boundary · 6 property · Production surface contract 2/2 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Parabolafit through (v,f(v)), (w,f(w)), (x,f(x))
Fallbackgolden section when the parabola is not acceptable
iMinimize only. This is not Dekker–Brent for f(x)=0. Polynomial coefficients are constant-first. Default tol = 10⁻⁸.

How to use

1

Enter integrand and [a, b]

Poly needs coeffs. a must be strictly less than b. Golden section lives on the sibling discovery URL.

2

Read xmin and fmin

An exact minimizer is shown when f is poly of degree ≤ 3, sin, or exp.

Example calculations

Common configurations with formula and result.

ϟ

min (x−1)² on [0, 3]

coeffs 1,−2,1

xmin = 1
1
ϟ

min sin on [π, 2π]

interior min

3π/2
4.712…

Brent Method calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Brent’s 1-D minimizer combines golden-section search with inverse parabolic interpolation on a bracket [a, b]. This page is method=brent on math.numerical.optimize_1d. Not Brent root-finding. Not a second optimizer.
What it calculates
xmin and fmin of poly, sin, or exp on [a, b] by Brent’s 1-D minimizer.
Inputs
  • integrand
  • a
  • b
  • tol?
  • coeffs?
Outputs
  • xmin
  • fmin
  • exact_xmin
  • exact_fmin
  • n_eval
Formula
Brent (golden section + inverse parabolic interpolation)
Assumptions
  • Minimize only
  • Not root-finding Brent, not Nelder–Mead, not CAS
Units
  • dimensionless
Boundary conditions
  • a ≥ b → INVALID_INPUT
  • unknown method (including nelder) → INVALID_MODE
Example
brent poly 1,-2,1 on [0,3] → xmin=1
Validation cases

2 published on this page · 11/11 tests · Production surface contract 2/2 · View evidence

  • integrand=poly coeffs=1,-2,1 a=0 b=3 → exact_xmin=1
  • method=nelder integrand=sin a=0 b=1 → INVALID_MODE
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Definite Integral Calculator, Gauss Quadrature Calculator, Golden Section Search Calculator, Numerical Derivative Calculator, Numerical Interpolation Calculator, Numerical Root Calculator, One-Dimensional Optimization Calculator, Simpson Rule Calculator . Explore all Numerical Calculus.

→ Definite Integral Calculator Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate. Runs locally. › → Gauss Quadrature Calculator n-point Gauss–Legendre quadrature of a polynomial, sin, or exp on [a, b]. Same engine as Definite Integral. Not indefinite CAS. Runs locally. › → Golden Section Search Calculator Golden-section search for a minimum of a polynomial, sin, or exp on [a, b]. Same engine as One-Dimensional Optimization. Not Brent, not multivariate. Runs locally. › → Numerical Derivative Calculator Finite-difference derivative of a polynomial, sin, or exp. Central, forward, or backward. Not symbolic d/dx. Runs locally. › → Numerical Interpolation Calculator Piecewise-linear, Lagrange, or natural cubic spline of tabulated (x, y). Not regression, not CAS. Runs locally. › → Numerical Root Calculator Find a real root of a polynomial with Newton, bisection, or secant. One capability, three methods. Not the nth-root page. Runs locally. › → One-Dimensional Optimization Calculator Minimize a polynomial, sin, or exp on [a, b] by golden-section search or Brent. Not multivariate, not max, not CAS. Runs locally. › → Simpson Rule Calculator Composite Simpson 1/3 of a polynomial, sin, or exp on [a, b]. Same engine as Definite Integral. Not indefinite CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this Brent’s method for roots?

No. Root-finding Brent is out of scope. This page minimizes a scalar on [a, b]. Numerical roots live on /calc/math/numerical-root.

Is this a second optimization engine?

No. It is method=brent on math.numerical.optimize_1d, the same engine as /calc/math/one-dimensional-optimization.