scholarly journals A FAST ALGORITHM FOR SOLVING LARGE SCALE MEAN-VARIANCE MODELS BY COMPACT FACTORIZATION OF COVARIANCE MATRICES

1992 ◽  
Vol 35 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Hiroshi Konno ◽  
Ken-ichi Suzuki
Keyword(s):  
Fast Algorithm ◽  
Large Scale ◽  
Covariance Matrices ◽  
Mean Variance

A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G25-G34 ◽  
Author(s):  
Saeed Vatankhah ◽  
Rosemary Anne Renaut ◽  
Vahid Ebrahimzadeh Ardestani
Keyword(s):  
Linear System ◽  
Singular Value Decomposition ◽  
Fast Algorithm ◽  
Large Scale ◽  
Gravity Data ◽  
Singular Values ◽  
Singular Value ◽  
System Matrix ◽  
Large Scale System ◽  
Value Decomposition

We develop a fast algorithm for solving the under-determined 3D linear gravity inverse problem based on randomized singular-value decomposition (RSVD). The algorithm combines an iteratively reweighted approach for [Formula: see text]-norm regularization with the RSVD methodology in which the large-scale linear system at each iteration is replaced with a much smaller linear system. Although the optimal choice for the low-rank approximation of the system matrix with [Formula: see text] rows is [Formula: see text], acceptable results are achievable with [Formula: see text]. In contrast to the use of the iterative LSQR algorithm for the solution of linear systems at each iteration, the singular values generated using RSVD yield a good approximation of the dominant singular values of the large-scale system matrix. Thus, the regularization parameter found for the small system at each iteration is dependent on the dominant singular values of the large-scale system matrix and appropriately regularizes the dominant singular space of the large-scale problem. The results achieved are comparable with those obtained using the LSQR algorithm for solving each linear system, but they are obtained at a reduced computational cost. The method has been tested on synthetic models along with real gravity data from the Morro do Engenho complex in central Brazil.

scholarly journals Estratégia Long-Short, Neutra ao Mercado, e Index Tracking Baseadas em Portfólios Cointegrados

2010 ◽  
Vol 8 (4) ◽  
pp. 469
Author(s):  
João Frois Caldeira ◽  
Marcelo Savino Portugal
Keyword(s):  
Ad Hoc ◽  
Tracking Error ◽  
Covariance Matrices ◽  
Return Level ◽  
Index Tracking ◽  
Optimal Portfolios ◽  
The Mean ◽  
Efficient Allocations ◽  
Mean Variance ◽  
Tracking Portfolios

The traditional models to optimize portfolios based on mean-variance analysis aim to determine the portfolio weights that minimize the variance for a certain return level. The covariance matrices used to optimize are difficult to estimate and ad hoc methods often need to be applied to limit or smooth the mean-variance efficient allocations recommended by the model. Although the method is efficient, the tracking error isn’t certainly stationary, so the portfolio can get distant from the benchmark, requiring frequent re-balancements. This work uses cointegration methodology to devise two quantitative strategies: index tracking and long-short market neutral. We aim to design optimal portfolios acquiring the asset prices’ co-movements. The results show that the devise of index tracking portfolios using cointegration generates goods results, replicating the benchmark’s return and volatility. The long-short strategy generated stable returns under several market circumstances, presenting low volatility.

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