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3411Why Richardson Extrapolation HelpsWhy does Richardson extrapolation often improve an estimate even when you never see the exact derivative value?数学中等essay未尝试面试订阅3412Why Smaller h Is Not Always BetterWhy can making h smaller eventually worsen a finite-difference estimate?数学中等essay未尝试面试订阅3413Why Diffusion Stability Scales With Delta x SquaredWhy does the explicit heat-equation time-step restriction shrink like Delta x squared rather than just like Delta x?数学中等essay未尝试面试订阅3414Why Boundary Conditions Change the StencilWhy can the same derivative operator require a different finite-difference stencil near a boundary than in the interior?数学中等essay未尝试面试订阅3415Why Central Differences Are Usually More Accurate Than One-Sided OnesWhy do central differences often achieve a higher order of accuracy than one-sided differences using similar nearby points?数学中等essay未尝试面试订阅4841Minimum Stable Mesh Width 1For the transformed heat equation u t = nu*u xx, an explicit scheme uses lambda = nu*Delta t/Delta x 2 and requires lambda <= 0.5. If nu=0.04 and Delta t=0.125, what is the smallest Delta x that keeps the scheme stable?数理金融简单数值题未尝试面试订阅4846Infer Explicit Update Weight 6A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=8, u up=9, u down=11, and u new=9. What lambda was used?数理金融简单数值题未尝试面试订阅4847Infer Explicit Update Weight 7A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=10, u up=12, u down=9, and u new=10.4. What lambda was used?数理金融简单数值题未尝试面试订阅4848Infer Explicit Update Weight 8A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=5, u up=6.5, u down=4.5, and u new=5.3. What lambda was used?数理金融简单数值题未尝试面试订阅4849Infer Explicit Update Weight 9A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=7, u up=8, u down=6.2, and u new=7.07. What lambda was used?数理金融简单数值题未尝试面试订阅4850Infer Explicit Update Weight 10A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=4.5, u up=5.5, u down=4, and u new=4.6. What lambda was used?数理金融简单数值题未尝试面试订阅4851Infer Rate From Crank-Nicolson Off-Diagonals 11Under the common Black-Scholes Crank-Nicolson convention alpha i = 0.25*Delta t*(sigma 2*i 2 - r*i) and gamma i = 0.25*Delta t*(sigma 2*i 2 + r*i). A grid dump reports i=2, Delta t=0.5, alpha i=0.0125, and gamma i=0.0275. What risk-free rate r is implied?数理金融中等数值题未尝试面试订阅4856Call Upper BoundaryIn a finite-difference grid for a European call, why is the far-right boundary often set close to S max - K e (-rτ) rather than to a constant?数理金融困难essay未尝试面试订阅4857Put Lower BoundaryWhy does a European put grid often impose V(0,τ) ≈ K e (-rτ) at the left boundary?数理金融困难essay未尝试面试订阅4858Negative WeightsWhy are explicit or theta-scheme weights turning negative a warning sign for an option grid, especially near kinks?数理金融困难essay未尝试面试订阅4859Nonuniform GridWhy can clustering grid points around the strike improve gamma estimates more than simply extending S max farther out?数理金融困难essay未尝试面试订阅4860Too Small TruncationIf S max is chosen too low in a call-pricing grid, what directional bias do you expect for deep in-the-money call values near the top of the grid, and why?数理金融困难essay未尝试面试订阅4861Infer Missing Upper Node From Delta 16At a stock grid with Delta S=5, the central-difference delta is approximated by Delta ≈ (V i+1 -V i-1 )/(2*Delta S). If V i-1 =12 and the desk wants Delta=0.8, what V i+1 is needed?数理金融中等数值题未尝试面试订阅4862Infer Center Node From Gamma 17At a stock grid with Delta S=2, the central-difference gamma is Gamma ≈ (V i+1 -2V i+V i-1 )/Delta S 2. If V i+1 =11, V i-1 =7, and the desk wants Gamma=0.5, what center value V i is needed?数理金融中等数值题未尝试面试订阅4863Infer Missing Lower Node From Delta 18At a stock grid with Delta S=1, the central-difference delta is Delta ≈ (V i+1 -V i-1 )/(2*Delta S). If V i+1 =9.4 and the target delta is 0.7, what V i-1 is implied?数理金融中等数值题未尝试面试订阅