In many applications that work on huge data sets, from areas like bioinformatics, data-mining, network analysis, optimization, and simulation, the computation time is a major concern. To shorten this time, we have to take into account the many aspects that determine the running time of a program on a modern computer. One of these aspects is the range of different type of memory, from fast but s...

Positive semidefinite matrix fields are becoming increasingly important in digital imaging. One reason for this tendency consists of the introduction of diffusion tensor magnetic resonance imaging (DTMRI). In order to perform shape analysis, enhancement or segmentation of such tensor fields, appropriate image processing tools must be developed. This paper extends fundamental morphological opera...

We consider two operations in the QTT format: composition of a multilevel Toeplitz matrix generated by a given multidimensional vector and convolution of two given multidimensional vectors. We show that low-rank QTT structure of the input is preserved in the output and propose efficient algorithms for these operations in the QTT format. For a d-dimensional 2n× . . .×2n-vector x given in a QTT r...

We introduce our Transform Imager Technology and Architecture. This approach allows for Retina and higher-level bio-inspired computation in a programmable architecture that still possesses similar high-fill factor pixels of APS imagers. This imager is capable of programmable matrix operations on the image, where we can represent the image as either a full matrix or using block matrix operations...

The LAPACK software project currently under development is intended to provide a portable linear algebra library for high performance computers. LAPACK will make use of the Level 1, 2, and 3 BLAS to carry out basic operations. A principal focus of this project is to implement blocked versions of a number of algorithms to take advantage of the greater parallelism and improved data locality of th...

Tensor computations–in particular tensor contraction (TC)–are important kernels in many scientific computing applications (SCAs). Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized implementations such as the BLAS, tensor operations have traditionally been implemented in terms of BLAS operations, incurring both a performance and a storage ...

Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Mo...

Array operations are useful in a large number of important scientific codes, such as molecular dynamics, finite element methods, climate modeling, atmosphere and ocean sciences, etc. In our previous work, we have proposed a scheme extended Karnaugh map representation (EKMR) for multidimensional array representation. We have shown that sequential multidimensional array operation algorithms based...