Michael W. Leonard

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Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly. It can be shown that the conventional BFGS method accumulates(More)
The molecular mechanisms specifying patterns of gene expression in the vertebrate brain, which in turn determine the developmental fates of specific neurons, are yet to be clearly defined. Individual members of a recently identified family of transcriptional regulatory proteins, the GATA factors, are required for the differentiation of certain hematopoietic(More)
Quasi-Newton methods are reliable and eecient on a wide range of problems, but they can require many iterations if no good estimate of the Hessian is available or the problem is ill-conditioned. Methods that are less susceptible to ill-conditioning can be formulated by exploiting the fact that quasi-Newton methods accumulate second-derivative information in(More)
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