Newton's method - Quiz
A) Newton's method B) Householder's method C) Halley's method D) Raphson's approximation
A) Isaac Newton and Joseph Raphson B) Joseph Raphson and Carl Friedrich Gauss C) Isaac Newton and Leonhard Euler D) Isaac Newton and Al-Khwarizmi
A) To calculate the derivative of a function B) To find the maximum value of a function C) To integrate a complex function D) To find a root of a function
A) Exact solutions without iteration B) Linear equations for curve fitting C) Better approximations to the roots of a function D) Larger derivatives of a function
A) A real-valued function B) A purely constant function C) A step function only D) An imaginary-valued function
A) Its second derivative and a final value B) Its derivative and an initial guess C) Its integral and two boundary points D) An exact root and a tolerance level
A) The local minimum of the function near x0 B) The y-intercept of the secant line at x0 C) The inflection point of the curve D) The x-intercept of the tangent line at (x0, f(x0))
A) The slope of the linear approximation B) The y-intercept of the linear approximation C) The maximum point of the linear approximation D) The unique root of the linear approximation
A) It increases linearly B) It triples with every step C) It roughly doubles D) It increases by a constant factor of two
A) Householder's methods B) Monte Carlo methods C) Euler's methods D) Runge-Kutta methods
A) Bisection method B) Secant method C) Halley's method D) Gradient descent
A) Only differential equations B) Discrete probability distributions C) Complex functions and systems of equations D) Only polynomial functions of degree two
A) The tangent line to the curve B) A horizontal line at f(xn) C) The vertical asymptote D) The secant line connecting the endpoints
A) f'(xn) cannot equal zero B) f'(xn) must be a complex number C) f'(xn) must equal zero D) f'(xn) must equal one
A) It generally requires fewer iterations to converge B) It diverges immediately C) It results in a division by zero D) It requires an infinite number of steps
A) At least quadratic B) Cubic C) Linear D) Logarithmic
A) They always diverge on real functions B) Extra computations required for each step C) They cannot be used on computers D) They require no derivatives at all
A) If the computer has too much memory B) If the initial guess is too close to the root C) If f or its derivatives are computationally expensive to evaluate D) If the function has too many roots
A) The sum of f(xn) and f'(xn) B) The derivative divided by the function itself C) The product of f(xn) and f'(xn) D) The ratio of f(xn) to f'(xn)
A) An initial guess B) The convergence threshold C) The exact final answer D) The absolute maximum
A) Old Babylonian period B) Golden Age of Athens C) Renaissance period D) Victorian era
A) 19th–16th century BCE B) 1st–2nd century CE C) 16th–17th century CE D) 9th–11th century CE
A) 1st–2nd century CE B) 9th–10th century CE C) 17th–18th century CE D) 19th–16th century BCE
A) Seki Kōwa B) Jamshīd al-Kāshī C) François Viète D) Sharaf al-Dīn al-Ṭūsī
A) 1680 B) 1427 C) 1711 D) 1633
A) 1135–1213 B) 1840–1900 C) 1540–1603 D) 973–1048
A) 973–1048 B) 1135–1213 C) 1633–1711 D) 1540–1603
A) John Wallis B) Henry Briggs C) Arthur Cayley D) Thomas Simpson
A) Seki Kōwa B) François Viète C) Joseph Raphson D) William Jones
A) 1135–1213 B) 1821–1895 C) 1540–1603 D) 1648–1725
A) Thomas Simpson B) John Colson C) Henry Briggs D) Arthur Cayley
A) 1711 B) 1687 C) 1671 D) 1669
A) John Colson B) John Wallis C) Joseph Raphson D) William Jones
A) 1690 B) 1669 C) 1685 D) 1671
A) John Wallis B) William Jones C) Thomas Simpson D) John Colson
A) Polynomials B) Logarithmic equations C) Differential equations D) Trigonometric equations
A) Complex roots B) Error corrections C) Derivative gradients D) Optimization factors
A) The linear coefficients B) Initial root estimates C) Constant terms D) Higher-degree terms
A) Geometric series B) Taylor series C) Fourier series D) Binomial series
A) Heat equation B) Wave equation C) Kepler's equation D) Euler's equation
A) Method of Fluxions B) Miftāḥ al-Ḥisāb C) De analysi per aequationes D) Philosophiæ Naturalis Principia Mathematica
A) 1711 B) 1687 C) 1633 D) 1740
A) François Viète B) Jamshīd al-Kāshī C) Sharaf al-Dīn al-Ṭūsī D) Seki Kōwa
A) An initial estimate B) The use of error corrections C) The use of polynomials D) The connection with calculus
A) John Wallis B) William Jones C) Joseph Raphson D) Thomas Simpson
A) Higher-degree terms B) The derivative function C) The original polynomial D) Taylor series expansion
A) A geometric optimization model B) A nonpolynomial Taylor series C) A complex root formula D) A reusable iterative expression
A) 1711 B) 1690 C) 1879 D) 1740
A) Finding roots of polynomials B) Extracting error corrections C) Solving optimization problems D) Approximating square areas
A) Arthur Cayley B) John Wallis C) Joseph Raphson D) Thomas Simpson
A) Faster B) Quadratic C) Slower D) The same
A) Linear interpolation B) Successive over-relaxation C) Removing the derivative D) Decreasing the number of iterations
A) The solution B) The multiplicity C) The derivative D) The initial error
A) m / x B) m * x C) x / m D) xm / m
A) Two iterations B) Ten iterations C) A single iteration D) Infinitely many iterations
A) Only for positive values B) Only for negative values C) No D) Yes
A) 1/2 x_n B) x_n2 C) 1/4 x_n D) 2 x_n
A) Exactly two B) Thousands C) Dozens D) Only one
A) Quadratic B) Superlinear but subquadratic C) Purely linear D) Cubic
A) About 4/3 B) About 2 C) About 1/2 D) About 10
A) Increasing rapidly B) Oscillating wildly C) Decreasing slowly D) Converging instantly
A) The 200th iterate B) The 2nd iterate C) The 10th iterate D) The 50th iterate
A) Linear behavior B) Undefined behavior C) Oscillatory behavior D) Convergent behavior
A) 0.06317 B) 1.00000 C) -1.76929 D) 0.99000
A) 1.00196 B) -0.06317 C) 0.03651 D) 1.00628
A) Iterates can be sent outside the domain B) Oscillation stops permanently C) The derivative becomes zero everywhere D) The method always converges faster
A) Universal B) Global C) Constant D) Local
A) Taylor's theorem B) Mean value theorem C) Intermediate value theorem D) Pythagorean theorem
A) xi + α B) xi / α C) xi - α D) α - xi
A) Undefined B) Zero C) Positive D) Negative
A) Undefined B) Negative C) Positive D) Zero
A) A tensor B) A scalar C) A vector D) A matrix
A) Matrix inversion B) Trigonometric operations C) Calculus integration D) Basic arithmetic operations
A) 612.5 B) 613.0 C) 305.5 D) 306.5
A) 10 decimal places B) 12 decimal places C) 5 decimal places D) 2 decimal places
A) 2mm B) 5mm C) 1mm D) 10mm
A) Maximum thickness B) Minimum height C) Maximum volume D) Minimum surface area
A) 1000 B) 1000000 C) 10000 D) 100000000
A) h + b + w = 1136000 B) hbw = 1136000 C) hbw = 2000000 D) 2hbW = 1136000
A) 1136000 / (hb) B) 1136000 * hb C) 1136000 / (h + b) D) 1136000 / w
A) [w, h] B) [b, w, h] C) [b, h] D) [w, b]
A) [50, 50] B) [100, 100] C) [1, 1] D) [0, 0]
A) [138.5684895, 65.67176536] B) [65.67176536, 138.5684895] C) [50.123, 110.456] D) [100, 100]
A) Identity matrix B) Hessian matrix C) Jacobian matrix D) Vector matrix
A) Derivatives B) Zeroes C) Asymptotes D) Integrals
A) Straight lines B) Circles C) Fractals D) Polygons
A) John Nash B) Richard Hamilton C) Curt McMullen D) Jürgen Moser
A) Euclidean space B) Hilbert space C) Banach space D) Fréchet space
A) Symmetric B) Strictly positive C) Boundedly invertible D) Continuously differentiable
A) 1960s B) 1940s C) 1970s D) 1950s
A) Universal starting points B) Smoothing operators C) Fréchet derivatives D) Complex initial conditions
A) 1980s B) 1960s C) 1950s D) 1970s
A) Complex analysis B) Celestial mechanics C) Fluid dynamics D) Quantum mechanics
A) John Nash B) Curt McMullen C) Richard Hamilton D) Jürgen Moser
A) Euclidean spaces B) Fréchet spaces C) Banach spaces D) Hilbert spaces
A) Second-order B) First-order C) Cubic D) Fourth-order
A) Maehly B) Pafnuty Chebyshev C) Newton D) Hensel
A) Chebyshev's method B) Quasi-Newton method C) Hensel's lemma D) Maehly's procedure
A) The set of primes B) The entire field C) The set of integers D) The unit ball
A) The Chebyshev analog B) The q-analog C) The Maehly analog D) The p-adic analog |
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