Matrix approximation refers to the process of finding a matrix that closely represents or approximates another matrix, typically under certain constraints or criteria. This concept is crucial in various applications, such as dimensionality reduction, noise reduction, and data compression, particularly when working with large datasets or ill-posed problems. One effective technique in achieving matrix approximation is through the use of truncated singular value decomposition (TSVD), which simplifies a complex matrix by retaining only its most significant singular values and corresponding singular vectors.
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