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Abstract Can one recover a matrix efficiently from only matrix‐vector products? If so, how many are needed? This article describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz‐like, and hierarchical low‐rank, from matrix‐vector products. In particular, we derive a randomized algorithm for recovering an unknown hierarchical low‐rank matrix from only matrix‐vector products with high probability, where is the rank of the off‐diagonal blocks, and is a small oversampling parameter. We do this by carefully constructing randomized input vectors for our matrix‐vector products that exploit the hierarchical structure of the matrix. While existing algorithms for hierarchical matrix recovery use a recursive “peeling” procedure based on elimination, our approach uses a recursive projection procedure.
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Improved efficiency of vibration-based sound power computation through multi-layered radiation resistance matrix symmetry
Computing sound power using complex-valued surface velocities involves using a geometry-dependent acoustic radiation resistance matrix multiplied by a velocity vector to compute sound power for a given frequency range. Using a laser scan grid with constant spacing and a scalar radiator area approximation, a multi-layered Toeplitz symmetry exists in the radiation resistance matrix. An innovative approach was developed to exploit this Toeplitz symmetry. This approach preserved accuracy and resulted in a maximum of ∼1300% computation time reduction for curved plate calculations and a ∼9600% computation time reduction for cylindrical shell sound power calculations.
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- Award ID(s):
- 1916696
- PAR ID:
- 10589320
- Publisher / Repository:
- Acoustical Society of America (ASA)
- Date Published:
- Journal Name:
- JASA Express Letters
- Volume:
- 2
- Issue:
- 12
- ISSN:
- 2691-1191
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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