Search results for "Linear"
showing 10 items of 7165 documents
Polynomial numerical indices of 𝐶(𝐾) and 𝐿₁(𝜇)
2013
We estimate the polynomial numerical indices of the spaces C ( K ) C(K) and L 1 ( μ ) L_1(\mu ) .
Inequalities for Information Potentials and Entropies
2020
We consider a probability distribution p0(x),p1(x),&hellip
Non-linear RLS-based algorithm for pattern classification
2006
A new non-linear recursive least squares (RLS) algorithm is presented in the context of pattern classification problems. The algorithm incorporates the non-linearity of the filter's output in the updating rules of the classical RLS algorithm. The proposed method yields lower stationary error levels when compared to the standard LMS and RLS algorithms in a classical application of pattern classification, such as the channel equalization problem.
A parallel radix-4 block cyclic reduction algorithm
2013
SUMMARY A conventional block cyclic reduction algorithm operates by halving the size of the linear system at each reduction step, that is, the algorithm is a radix-2 method. An algorithm analogous to the block cyclic reduction known as the radix-q partial solution variant of the cyclic reduction (PSCR) method allows the use of higher radix numbers and is thus more suitable for parallel architectures as it requires fever reduction steps. This paper presents an alternative and more intuitive way of deriving a radix-4 block cyclic reduction method for systems with a coefficient matrix of the form tridiag{ − I,D, − I}. This is performed by modifying an existing radix-2 block cyclic reduction me…
Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition
2014
A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model is reported. It employs a Cholesky decomposition of the two-electron integrals that significantly reduces the computational cost and the storage requirements of the method compared to standard implementations. Our algorithm also exploits a partitioning form of the CC2 equations which reduces the dimension of the problem and avoids the storage of doubles amplitudes. We present calculation of excitation energies of benzene using a hierarchy of basis sets and compare the results with conventional CC2 calculations. The reduction of the scaling is evaluated as well as the effect of the Cholesky …
On the intrinsic complexity of learning
1995
A new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.
Energy-weighted M1 sum rule with explicit δ degrees of freedom
1985
Abstract The influence of Δ degrees of freedom on the energy-weighted M1 sum rule is investigated and applied to 2 H and 4 He. Using π- and ρ-exchange potentials a reduction of the potential contribution of the order of 50% is obtained. The absolute value of the sum rule is strongly dependent on the short-range behaviour of the nuclear wave function. Furthermore, the contribution of c.m. effects is evaluated and found to be of the order of 5–10%.
Artificial Ground Motions and Nonlinear Response of RC Structures
2020
The selection of seismic inputs for nonlinear dynamic analysis is widely debated, mainly focusing on the advantages and disadvantages provided by the choice of natural, simulated, or artificial records. This work proves the differences in the structural behavior of RC buildings when using accelerograms with different levels of stationarity. Initially, nonlinear response under three sets of accelerograms equivalent in terms of pseudo acceleration spectrum is evaluated and compared. Then, the results of incremental dynamic analyses are compared by the statistical point of view considering different levels of irregularity for the reference structure.
Self-calibration of a PTZ Camera Using New LMI Constraints
2013
In this paper, we propose a very reliable and flexible method for self-calibrating rotating and zooming cameras - generally referred to as PTZ (Pan-Tilt-Zoom) cameras. The proposed method employs a Linear Matrix Inequality (LMI) resolution approach and allows extra tunable constraints on the intrinsic parameters to be taken into account during the process of estimating these parameters. Furthermore, the considered constraints are simultaneously enforced in all views rather than in a single reference view. The results of our experiments show that the proposed approach allows for significant improvement in terms of accuracy and robustness when compared against state of the art methods.
Fitting linear models and generalized linear models with large data sets in R
2009
We present an estimating algorithm to fit linear and generalized linear models not involving the QR decomposition. Some new R functions are presented and discussed. For large data sets, comparisons with respect to the well-known lm() and glm(), as well as to biglm() and bigglm() from the package biglm, show that the proposed functions speed up computation while preserving numerical stability and accuracy