Related papers: Revisiting the D-iteration method: from theoretica…
Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes…
Conditional gradient methods (CGM) are widely used in modern machine learning. CGM's overall running time usually consists of two parts: the number of iterations and the cost of each iteration. Most efforts focus on reducing the number of…
In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
This note provides a simple example demonstrating that, if exact computations are allowed, the number of iterations required for the value iteration algorithm to find an optimal policy for discounted dynamic programming problems may grow…
Online learning makes sequence of decisions with partial data arrival where next movement of data is unknown. In this paper, we have presented a new technique as multiple times weight updating that update the weight iteratively forsame…
This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the computational problem among…
We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
Eigenfactor.org, a journal evaluation tool which uses an iterative algorithm to weight citations (similar to the PageRank algorithm used for Google) has been proposed as a more valid method for calculating the impact of journals. The…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…