Revision #865 → #1425 · back to history
addedNewton's method (root-finding algorithm)9a74de0aa035
addedGeometric interpretation as tangent x-intercept52e5d0d64428
addedTangent-line linear approximation1820464b3a14
addedQuadratic convergence at simple rootd811d708380d
addedModified algorithm for known multiplicity m0524ee76d12c
addedg(x)=f/f' has simple root at same location53ca5c30a7a3
addedf(x)=x^2 — linear convergencee2b122b61b8e
addedf(x)=x+x^{4/3} — superlinear subquadratic42f9f5a13a72
addedf(x)=x^{20}-1 — slow start then quadraticdd1e9e14c556
addedf(x)=x(1+x^2)^{-1/2} — trichotomy of behaviord2deb10e2f20
addedSubtle initialization dependence with multiple roots5204fff67088
addedf(x)=x^{1/3} — divergence near root0adef758b2c9
addedf(x)=x^{1/3}e^{-x^2} — false stopping-criterion failureb68285dd7559
addedOscillation for f(x)=x^3-2x+2f21e6c89ceb0
addedUndefined iterate for f(x)=x^2-1 at 059c8f6a36f9c
addedNatural logarithm — domain escapef2ad6ef56030
addedLocal convergence with nonzero derivative832a4d4b4c18
addedQuadratic-or-faster convergence under C^2c6f7d6f6f2ec
addedLinear convergence with rate 1/2 when f'(α)=035e044b624e3
addedLinear convergence for zero of multiplicity ra1e756149f3c
addedGlobal monotonic convergence on right neighborhoodb749bc1c374c
addedQuadratic convergence proof via Taylor's theorem94634dd4da0e
addedFourier — Newton iteration converges from left endpoint2d5f470b8c7b
addedFourier's modified Newton iteration from right endpoint88fc89934c34
addedQuadratic convergence of left-right difference72ce70fdcf5d
addedError vector and Hessian quadratic form (n>1)27512fb57f2c
addedSquare root via Newton's method (Babylonian)3a24b0d3e858
addedSolving cos(x) = x^30a27eec57b6e
addedNewton's method for k equations via Jacobian inverse12943c0a898f
addedGeneralized inverse Newton for overdetermined systems11745d6c39fb
addedMilk carton minimum surface area1c8b3ac65ca6
addedBasin of attraction for complex zeroes8c4762b2d2d4
addedReal iterates cannot reach non-real roots of x^2+1f10753e2f4be
addedMcMullen — divergence for degree ≥ 4 polynomials77685d717021
addedHubbard–Schleicher–Sutherland initial-point set38ec18531dd3
addedNewton's method in a Banach space (Fréchet derivative)8b2edf03073e
addedNewton–Kantorovich theoreme35f11fb6557
addedNash–Moser smoothed Newton iteration21e03d558a7a
addedQuasi-Newton methodba8691d8f0b1
addedChebyshev's third-order method522e62cbacef
addedHensel's lemma — p-adic Newton recursion80a73b9f444c
addedq-analog of Newton's methodea0961ab6791
addedMaehly's procedure for next rootf7ac16cdcc95
addedHirano's modified Newton methodabfa8c29f5bf
addedInterval Newton operator9e24446ed799
addedInterval Newton — root containment and halving8493880014af
addedExtended interval division separates multiple roots1402eaccd2ea
addedNewton's method applied to f' for optimizationece892e8ecac
addedNewton–Raphson division (reciprocal of a)21e61c7942fe
addedTranscendental equations — inverse Normal CDF9a3ce327c5d3
addedNumerical verification by candidate sets32db0385c6f8
addedPython implementation for f(x)=x^2-249fadb53fe51