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A note on direct methods for approximations of sparse Hessian matrices

Miroslav Tůma (1988)

Aplikace matematiky

Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.

A parallel projection method for linear algebraic systems

Fridrich Sloboda (1978)

Aplikace matematiky

A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.

A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

Douglas Bunker, Lixing Han, Shu Hua Zhang (2013)

Applications of Mathematics

The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions....

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