Corpus ID: 119687366

A New Numerical Method for Fast Solution of Partial Integro-Differential Equations

@article{Dourbal2016ANN,
  title={A New Numerical Method for Fast Solution of Partial Integro-Differential Equations},
  author={Pavel Dourbal and Mikhail Pekker},
  journal={arXiv: Numerical Analysis},
  year={2016}
}
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical methods… Expand
2 Citations

Figures and Tables from this paper

Fast algorithm synthesis for arbitrary linear transforms
A method of fast algorithm synthesis for an arbitrary linear transform is proposed. The method is based on factorization of a linear transform operator and using the factors for buildingExpand
Synthesis of fast multiplication algorithms for arbitrary tensors
TLDR
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector for fast tensor - vector multiplication on a computer or dedicated hardware platform is proposed. Expand

References

SHOWING 1-9 OF 9 REFERENCES
Iterative methods for sparse linear systems
  • Y. Saad
  • Computer Science, Mathematics
  • 2003
TLDR
This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book. Expand
Partial and Total Matrix Multiplication
TLDR
By combining Pan’s trilinear technique with a strong version of the compression theorem for the case of several disjoint matrix multiplications it is shown that multiplication of N \times N matrices (over arbitrary fields) is possible in time. Expand
Synthesis of fast multiplication algorithms for arbitrary tensors
TLDR
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector for fast tensor - vector multiplication on a computer or dedicated hardware platform is proposed. Expand
Matrix multiplication via arithmetic progressions
We present a new method for accelerating matrix multiplication asymptotically. Thiswork builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. WeExpand
Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations
  • V. Pan
  • Mathematics, Computer Science
  • 19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
  • 1978
A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear non-commutative algorithms for matrix multiplication. The result isExpand
Finding, Minimizing, and Counting Weighted Subgraphs
TLDR
To obtain these algorithms for computing the permanent of a $k \times n$ matrix over rings and semirings, the $O^*$ notation omits $poly(k)$ factors. Expand
Method and apparatus for fast digital filtering and signal processing." US Patent Application
  • 2015
2 n O complexity for approximate matrix multiplication
  • 1979
  7799 . 2 nO complexity for approximate matrix multiplication ” . —
  • Inform . Process . Lett .
  • 1979