wilkinson

Wilkinson's eigenvalue test matrix

Syntax

W = wilkinson(n)

W = wilkinson(n,typename)

Description

W = wilkinson(n) returns one of J. H. Wilkinson's n-by-n eigenvalue test matrices. W is a symmetric, tridiagonal matrix with pairs of nearly equal eigenvalues.

W = wilkinson(n,typename) returns a matrix of type typename, which can be "single" or "double".

Examples

Wilkinson Test Matrix

Compute a 7-by-7 Wilkinson eigenvalue test matrix. The most frequently used case is wilkinson(21), whose two largest eigenvalues are approximately 10.746. The eigenvalues agree to 14, but not 15, decimal places.

W = wilkinson(7)

W = 7×7

     3     1     0     0     0     0     0
     1     2     1     0     0     0     0
     0     1     1     1     0     0     0
     0     0     1     0     1     0     0
     0     0     0     1     1     1     0
     0     0     0     0     1     2     1
     0     0     0     0     0     1     3

Input Arguments

n — Matrix order

scalar, nonnegative integer

Matrix order, specified as a scalar, nonnegative integer.

Example: wilkinson(10)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char

typename — Matrix data type

"double" (default) | "single"

Matrix data type, specified as either "double" or "single".

Example: wilkinson(10,"single")

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• n must be a fixed-size scalar.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Refer to the usage notes and limitations in the C/C++ Code Generation section. The same usage notes and limitations apply to GPU code generation.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The wilkinson function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a