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Solving matrix equations stands as a pivotal component of linear algebra, finding widespread applications in signal processing, scientific computing, and the second-order training of neural networks. Matrix inversion is notably more sensitive to input errors compared to conventional matrix multiplication, necessitating an exceptionally high level of computational precision. Nevertheless, digital approaches to achieve high-precision matrix inversion are computationally expensive, with time complexity escalating to cubic levels. As big data applications continue to proliferate, such highly complex computations present formidable challenges to traditional digital computers. This challenge becomes especially pressing as traditional device sizes near their physical limits and the Von Neumann architecture grapples with the 'memory wall' bottleneck.
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