matrix decomposition - 2024 Penn Bowl Harvard

Question

A form of this process is commonly used to solve linear least squares problems. For 10 points each:

[10m] Name this process, also known as matrix factorization. Common types of this process are named “LU” (“L-U”) and “QR.”

ANSWER: matrix decomposition [accept LU decomposition; accept QR decomposition]

[10h] This doubly eponymous method of finding QR decompositions is numerically unstable, but is the only method applicable for iterative methods, because it produces the jth orthonormalized vector after the jth iteration.

ANSWER: Gram-Schmidt process [accept Gram-Schmidt orthonormalization; reject “Gram-Schmidt orthogonalization”]

[10e] The Gram-Schmidt process involves applying this linear transformation to a vector. Graphically, this transformation is equivalent to displaying a 3-dimensional object on a 2-dimensional space.

ANSWER: projection

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Summary


2024 Penn Bowl Berkeley	11/02/2024	Y	2	25.00	100%	100%	50%
2024 Penn Bowl CWRU	11/02/2024	Y	2	20.00	100%	100%	0%
2024 Penn Bowl Chicago	11/02/2024	Y	8	20.00	88%	63%	50%
2024 Penn Bowl Florida	10/26/2024	Y	2	30.00	100%	100%	100%
2024 Penn Bowl Harvard	10/26/2024	Y	3	23.33	100%	67%	67%
2024 Penn Bowl Mainsite	11/02/2024	Y	3	16.67	67%	67%	33%
2024 Penn Bowl Playtest	10/12/2024	Y	2	25.00	100%	100%	50%
2024 Penn Bowl Texas	11/02/2024	Y	2	15.00	50%	50%	50%
2024 Penn Bowl UK	10/26/2024	Y	5	24.00	100%	100%	40%
2024 Penn Bowl UNC	10/26/2024	Y	3	26.67	100%	100%	67%

Data


Harvard A	Yale A	10	10	10	30
MIT	BU	10	10	10	30
Brandeis	Tufts	0	0	10	10