# 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…

## 2 Citations

### Fast algorithm synthesis for arbitrary linear transforms

- Computer Science, Engineering2017 Computing Conference
- 2017

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 building…

### Synthesis of fast multiplication algorithms for arbitrary tensors

- Computer Science, EngineeringArXiv
- 2016

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.

## References

SHOWING 1-9 OF 9 REFERENCES

### Iterative methods for sparse linear systems

- Computer Science
- 2003

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.

### Applied Iterative Methods

- Physics
- 2007

This book is the first book to combine subjects such as optimization, convex analysis, and approximation theory and organize them around a detailed and mathematically sound treatment of iterative algorithms.

### Partial and Total Matrix Multiplication

- Mathematics, Computer ScienceSIAM J. Comput.
- 1981

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.

### Matrix multiplication via arithmetic progressions

- MathematicsSTOC
- 1987

A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.

### Synthesis of fast multiplication algorithms for arbitrary tensors

- Computer Science, EngineeringArXiv
- 2016

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.

### Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations

- Computer Science19th 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 is…

### Finding, minimizing, and counting weighted subgraphs

- Computer Science, MathematicsSTOC '09
- 2009

These algorithms rely on fast algorithms for computing the permanent of a k x n matrix, over rings and semirings and give a new (algorithmic) application of multiparty communication complexity.

### Method and apparatus for fast digital filtering and signal processing." US Patent Application

- 2015

### 7799 . 2 nO complexity for approximate matrix multiplication ” . —

- Inform . Process . Lett .
- 1979