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