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• How many continuous derivatives does a natural cubic spline have at its knots?Numerical methods · Foundation
• You halve the step size in the trapezoid rule. By what factor does the error fall?Numerical methods · Foundation
• What is machine epsilon for IEEE 754 double precision, in units of 10⁻¹⁶, to…Numerical methods · Foundation
• Newton’s method for x²−2 = 0 starts at x₀ = 1. What is x₂, to four decimals?Numerical methods · Foundation
• Apply one Newton step to f(x) = x³−2x−5 starting from x₀ = 2. What is x₁?Numerical methods · Foundation
• The two-year yield is 3.0% and the five-year 3.6%.Numerical methods · Foundation
• Estimate ∫₀¹x² dx with the trapezoid rule on two equal intervals.Numerical methods · Foundation
• For [[4, 1], [1, 3]]x = [1, 2], one Jacobi iteration from x = (0,0) gives what…Numerical methods · Foundation
• A finite-difference grid has 1,000 price points by 1,000 time steps, stored as float64.Numerical methods · Foundation
• Solve y' = y, y(0) = 1 with forward Euler and step h = 0.5. What is the estimate of y(1)?Numerical methods · Foundation
• What is the global order of accuracy of the classical fourth-order Runge–Kutta method?Numerical methods · Foundation
• Stepping the heat equation, part 1 of 3Numerical methods · Foundation
• Newton’s method for a square root, part 1 of 3Numerical methods · Foundation
• Integrating an exponential, part 1 of 3Numerical methods · Foundation
• Where doubles run out of digits, part 1 of 3Numerical methods · Foundation
• Starting from the bracket [0,5], how many bisection steps are needed to locate…Numerical methods · Applied · Free solution
• An at-the-money one-year call on a $100 stock trades at $8, with rates at zero.Numerical methods · Applied · Free solution
• Why do exchange systems store prices as integer ticks rather than as…Numerical methods · Applied
• A Monte Carlo price has a standard error of 0.04 after 10⁴ paths.Numerical methods · Applied
• Why interpolate a yield curve with cubic splines rather than a single…Numerical methods · Applied
• Newton’s method converges quadratically and you start with one correct digit.Numerical methods · Applied
• Up to what polynomial degree does three-point Gauss–Legendre quadrature integrate exactly?Numerical methods · Applied
• Roughly how many floating-point operations does a Cholesky factorisation of a…Numerical methods · Applied
• What is the order of accuracy in time of the Crank–Nicolson scheme?Numerical methods · Applied
• Iterating xₖ₊₁ = cos xₖ converges to the fixed point x* ≈ 0.739.Numerical methods · Applied
• Why is Brent’s method a common default root-finder in numerical libraries?Numerical methods · Applied
• A quadratic passes through (0,1), (1,3) and (2,7). What is its value at x = 1.5?Numerical methods · Applied
• Estimate ∫₀¹x³ dx with Simpson’s rule on two equal intervals.Numerical methods · Applied
• For a smooth function, how does the error of the midpoint rule compare with…Numerical methods · Applied
• You solve Ax = b in double precision (about 16 significant digits) and A has…Numerical methods · Applied
• Why does Gaussian elimination use partial pivoting?Numerical methods · Applied
• An explicit scheme for the advection equation uₜ+2uₓ = 0 uses Δx = 0.01.Numerical methods · Applied
• In double precision, what does 1 - math.cos(1e-8) evaluate to?Numerical methods · Applied
• Double precision can represent every integer up to 2ᵏ exactly, but not every…Numerical methods · Applied
• A loop total = 0.0; for _ in range(10): total += 0.1 leaves total == 0.9999999999999999.Numerical methods · Applied
• Stepping the heat equation, part 2 of 3Numerical methods · Applied
• Newton’s method for a square root, part 2 of 3Numerical methods · Applied
• Integrating an exponential, part 2 of 3Numerical methods · Applied
• Where doubles run out of digits, part 2 of 3Numerical methods · Applied
• Your implied-volatility solver uses pure Newton–Raphson. Which input breaks it?Numerical methods · Advanced