In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload of an arbitrary polynomial function some massive private matrices (inputs) cluster workers. The workers are not reliable. Some them may collude gain information about input data (semi-honest workers). system initialized by sharing (randomized) each matrix server. Since massive, share's size...

Provenance is well-understood for relational query operators. Increasingly, however, data analytics is incorporating operations expressed through linear algebra: machine learning operations, network centrality measures, and so on. In this paper, we study provenance information for matrix data and linear algebra operations. Our core technique builds upon provenance for aggregate queries and cons...

Recently, an algorithm-based approach using diskless checkpointing has been developed to provide fault tolerance for high-performance matrix operations. With this approach, since fault tolerance is incorporated into the matrix operations, the matrix operations become resilient to any single processor failure or change with low overhead. In this paper, we present a technique called multiple chec...

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.

this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matri...