Question
When performing this method, the top left element of the reduction matrix is set equal to the square root of the top left element of the original matrix during each iteration. For 10 points each:
[10h] Name this method, which finds a matrix A such that A times A-transpose equals a covariance matrix, like that in fractional Brownian motion. This method typically creates a lower triangular matrix A.
ANSWER: Cholesky factorization [or Cholesky decomposition; prompt on LU decomposition or LU factorization or lower-upper decomposition or lower-upper factorization by asking “what special case of that factorization?”]
[10m] The Cholesky factorization decomposes matrices with this property into a lower triangular matrix and its transpose. This condition holds for a matrix M if for every real vector x, x-transpose times M times x is strictly greater than zero.
ANSWER: positive definite [or PD; accept symmetric positive definite or SPD; reject “positive semidefinite”]
[10e] The number of operations required for Cholesky factorization is roughly half the number of an “elimination” named for this German mathematician, who also names the normal distribution.
ANSWER: Carl Friedrich Gauss [or Johann Carl Friedrich Gauss; accept Gaussian elimination; accept Gaussian distribution]
<KJ, Other Science: Math>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 3 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 10.00 | 80% | 20% | 0% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 10.00 | 100% | 0% | 0% |
Data
| Berkeley B | Stanford A | 0 | 10 | 10 | 20 |
| Berkeley A | Berkeley C | 0 | 10 | 10 | 20 |