Mathematics and Optimization

R2026b

Accelerate solving linear algebra and optimization problems with parallel computing

Use parallel computing to accelerate solving linear algebra and optimization problems, including solving linear system, linear, quadratic, conic, integer, and nonlinear optimization problems, and searching for global solutions to problems that contain multiple maxima or minima.

Topics

Linear Algebra

Accelerate Solving Linear Equations Using GPU
This example shows how to speed up solving systems of linear equations using a GPU.
Work with Sparse Arrays on a GPU
Learn about the conditions for working with sparse arrays on a GPU.
Use Distributed Arrays to Solve Systems of Linear Equations with Direct Methods
This example shows how to solve a system of linear equations of the form $A x = b$ in parallel with a direct method using distributed arrays.
Use Distributed Arrays to Solve Systems of Linear Equations with Iterative Methods
For large-scale mathematical computations, iterative methods can be more efficient than direct methods.

Optimization

Parallel Computing in Optimization Toolbox (Optimization Toolbox)
Use multiple processors for optimization.
Testing Parallel Computing (Optimization Toolbox)
Verify that your problem runs correctly in parallel.
Improving Performance with Parallel Computing (Optimization Toolbox)
Investigate factors for speeding optimizations.

Global Optimization

Parallel Computing with MultiStart and GlobalSearch (Global Optimization Toolbox)
Distribute start points across processors with MultiStart, or use parallel gradient estimation with GlobalSearch.
Parallel Computing in Global Optimization Toolbox (Global Optimization Toolbox)
Use multiple processors to speed optimization.
Optimize ODEs in Parallel (Global Optimization Toolbox)
Save time by calling an expensive subroutine just once and computing an ODE solution in parallel using patternsearch or ga.

Related Information

Functions with Automatic Parallel Support (Optimization Toolbox)
Functions with Automatic Parallel Support (Global Optimization Toolbox)

Featured Examples

Solve Differential Equation Using Multigrid Preconditioner on Distributed Discretization

Solve Poisson's equation using a preconditioned iterative solver and distributed arrays. By using distributed arrays, you can scale up the calculation using the memory of a cluster of machines, not just the memory of a single machine. You can scale up without changing your code.