Rounding Errors in Algebraic Processes

By Xiaomei Yang. 1964

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Citations in the corpus

Privacy-Preserving Ridge Regression on Hundreds of Millions of Records (2013, background): “In particular, it is well suited for fixed point number representations [37].”
A GENERAL PROGRAM FOR ITEM‐RESPONSE ANALYSIS THAT EMPLOYS THE STABILIZED NEWTON–RAPHSON ALGORITHM (2013, background): “The Cholesky decomposition LiL ′ 2 i = −∇ Li(θim) (80) is available for a unique K by K matrix Li such that, for 1 ≤ k ≤ K and 1 ≤ k′ ≤ K, row k and column k′ is 0 if k k′ and row k and column k is nonnegative (Wilkinson, 1963, pp. 117–120).”
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem (2006, unknown): “What really happens here [77] is that we are effectively solving a problem perturbed by some small ε > 0; the “approximate solution” xi (ε),y ∗ i (ε) ∈ Ri (i = 1, 2, 3) is really a solution to the perturbed problem”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, unknown): “Historically, the ﬁrst application of related techniques was to ﬁnding distinct roots of scalar polynomials [53, pp. 78].”
Much Faster Algorithms for Matrix Scaling (2017, background): “The matrix ( r, c )-scaling problem is so natural and important that it was discovered independently by many diﬀerent scientiﬁc communities, starting in 1937 with the work of Kruithof [20] in telephone forecasting, Deming and Stephan [10] in transportation science, Brown [8] in engineering, Stone [3”
Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods (2017, methodology): “The literature on these problems [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15] is truly extensive and dates back to 1960s.”