Rank-Deficient and Discrete Ill-Posed Problems

Rank-Deficient and Discrete Ill-Posed Problems

March 27, 2011 | Unknown Author
Corrections have been made to address misprints in both the first and second printings of the text. In the second printing, on page 59, equation (3.37), the dagger symbol was removed from the matrix expression. On page 83, equation (4.34), the variable in the equation was changed from $ u_i^T b $ to $ u_j^T b $. On page 86, a mathematical expression was corrected to remove the square of the summation. On page 87, a term in the equation was updated from $ \ell \sigma_0/(s \lambda) $ to $ \ell \sigma_0/(2 \lambda) $. On page 95, a value in the figure caption was changed from $ 10^{-1} $ to $ 5 \cdot 10^{-3} $. On page 102, an illustration of the annihilation process had a missing '0' corrected. On page 147, the caption for figure 6.2 was updated to change $ \sigma_i $ to $ \sigma_i^2 $. On page 184, a reference to figure 7.2 was corrected to figure 7.1. On page 213, a formula was updated to include real parts in the variables. In the first printing, on page 8, a range of numbers was corrected from $ 0,\ldots,q $ to $ 0,\ldots,p $. On page 38, a sentence was replaced with a reference to a MATLAB package. On page 43, a norm was corrected from $ \|A\|_F $ to $ \|A\|_F^2 $. On page 54, a norm was updated from $ \|AT - A^{exact}\|_2 $ to $ \|AT - A^{exact}\|_F $. On page 70, an equation was corrected to use $ e $ instead of $ b $. On page 71, two instances of $ b $ were changed to $ e $. On page 87, the square root in an equation was replaced with $ \sigma_0 \sqrt{m - n + p} $. On page 97, three equations were added to replace a single equation. On page 117, a matrix dimension was corrected. On page 120, an equation was updated to define the total variation norm. On page 121, a term was corrected to refer to constant pieces. On page 184, a limit was corrected from $ n \rightarrow \infty $ to $ m \rightarrow \infty $. On page 209, a version number was updated. On page 211, two algorithm names were changed. On pages 217–242, severalCorrections have been made to address misprints in both the first and second printings of the text. In the second printing, on page 59, equation (3.37), the dagger symbol was removed from the matrix expression. On page 83, equation (4.34), the variable in the equation was changed from $ u_i^T b $ to $ u_j^T b $. On page 86, a mathematical expression was corrected to remove the square of the summation. On page 87, a term in the equation was updated from $ \ell \sigma_0/(s \lambda) $ to $ \ell \sigma_0/(2 \lambda) $. On page 95, a value in the figure caption was changed from $ 10^{-1} $ to $ 5 \cdot 10^{-3} $. On page 102, an illustration of the annihilation process had a missing '0' corrected. On page 147, the caption for figure 6.2 was updated to change $ \sigma_i $ to $ \sigma_i^2 $. On page 184, a reference to figure 7.2 was corrected to figure 7.1. On page 213, a formula was updated to include real parts in the variables. In the first printing, on page 8, a range of numbers was corrected from $ 0,\ldots,q $ to $ 0,\ldots,p $. On page 38, a sentence was replaced with a reference to a MATLAB package. On page 43, a norm was corrected from $ \|A\|_F $ to $ \|A\|_F^2 $. On page 54, a norm was updated from $ \|AT - A^{exact}\|_2 $ to $ \|AT - A^{exact}\|_F $. On page 70, an equation was corrected to use $ e $ instead of $ b $. On page 71, two instances of $ b $ were changed to $ e $. On page 87, the square root in an equation was replaced with $ \sigma_0 \sqrt{m - n + p} $. On page 97, three equations were added to replace a single equation. On page 117, a matrix dimension was corrected. On page 120, an equation was updated to define the total variation norm. On page 121, a term was corrected to refer to constant pieces. On page 184, a limit was corrected from $ n \rightarrow \infty $ to $ m \rightarrow \infty $. On page 209, a version number was updated. On page 211, two algorithm names were changed. On pages 217–242, several
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