Quant interview questions

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• 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
• A Monte Carlo price has a standard error of 0.04 after 10⁴ paths.Numerical methods · Applied
• Roughly how many floating-point operations does a Cholesky factorisation of a…Numerical methods · Applied
• Iterating xₖ₊₁ = cos xₖ converges to the fixed point x* ≈ 0.739.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
• A loop total = 0.0; for _ in range(10): total += 0.1 leaves total == 0.9999999999999999.Numerical methods · Applied
• You need x = A⁻¹b. Why does production code not compute the inverse?Numerical methods · Advanced
• Computing a variance as 𝔼[X²]−(𝔼[X])² sometimes returns a small negative number. Why?Numerical methods · Advanced
• You sum ten million small positive numbers in float32. What goes wrong and what fixes it?Numerical methods · Advanced
• Linear interpolation of eˣ on an interval of width h = 0.1 starting at 0 has…Numerical methods · Advanced
• Trapezoid estimates of ∫₀¹x² dx are 0.375 with step h and 0.34375 with step h/2.Numerical methods · Advanced