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YCor
YCor
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Matrix Quantizationquantization and Effecteffect on Singular Valuessingular values

Corrected spelling in title, improved grammar
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gmvh
gmvh
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Matrix Quantization and Effect on SignularvaluesSingular Values

Let $A$ and $B$ be an $N\times n$ matrix with $n\le N$, and let $\sigma_1(X),\dots \sigma_n(X)$ denote the singular values of $X\in \{A,B\}$. Do we have upper and lower bounds for $$ \| \sigma_i(A)-\sigma_i(B) \| $$ as a function of $\|A-B\|$ (for some matrix norm $\|\cdot\|$)?

Matrix Quantization and Effect on Signularvalues

Let $A$ and $B$ be an $N\times n$ matrix with $n\le N$ let $\sigma_1(X),\dots \sigma_n(X)$ denote the singular values of $X\in \{A,B\}$. Do we have upper and lower bounds for $$ \| \sigma_i(A)-\sigma_i(B) \| $$ as a function of $\|A-B\|$ (for some matrix norm $\|\cdot\|$)?

Matrix Quantization and Effect on Singular Values

Let $A$ and $B$ be an $N\times n$ matrix with $n\le N$, and let $\sigma_1(X),\dots \sigma_n(X)$ denote the singular values of $X\in \{A,B\}$. Do we have upper and lower bounds for $$ \| \sigma_i(A)-\sigma_i(B) \| $$ as a function of $\|A-B\|$ (for some matrix norm $\|\cdot\|$)?

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ABIM
ABIM
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Matrix Quantization and Effect on Signularvalues

Let $A$ and $B$ be an $N\times n$ matrix with $n\le N$ let $\sigma_1(X),\dots \sigma_n(X)$ denote the singular values of $X\in \{A,B\}$. Do we have upper and lower bounds for $$ \| \sigma_i(A)-\sigma_i(B) \| $$ as a function of $\|A-B\|$ (for some matrix norm $\|\cdot\|$)?