Wilson matrix is the following matrix having integers as elements:[1][2][3][4][5]
This is the coefficient matrix of the following system of linear equations considered in a paper by J. Morris published in 1946:[6]
Morris ascribes the source of the set of equations to one T. S. Wilson but no details about Wilson have been provided. The particular system of equations was used by Morris to illustrate the concept of ill-conditioned system of equations. The matrix has been used as an example and for test purposes in many research papers and books over the years. John Todd has referred to as “the notorious matrix W of T. S. Wilson”.[1]
has the factorisation with as the integer matrix[7].
Research problems spawned by Wilson matrix
A consideration of the condition number of the Wilson matrix has spawned several interesting research problems relating to condition numbers of matrices in certain special classes of matrices having some or all the special features of the Wilson matrix. In particular, the following special classes of matrices have been studied:[1]
the set of nonsingular, symmetric matrices with integer entries between 1 and 10.
the set of positive definite, symmetric matrices with integer entries between 1 and 10.
An exhaustive computation of the condition numbers of the matrices in the above sets has yielded the following results:
Among the elements of , the maximum condition number is and this maximum is attained by the matrix .
Among the elements of , the maximum condition number is and this maximum is attained by the matrix .
^Cleve Moler.
"Reviving Wilson's Matrix". Cleve’s Corner: Cleve Moler on Mathematics and Computing. MathWorks. Retrieved 24 May 2022.
^Carl Erik Froberg (1969). Introduction to Numerical Analysis (2 ed.). Reading, Mass.: Addison-Wesley.
^Robert T Gregory and David L Karney (1978). A Collection of Matrices for Testing Computational Algorithms. Huntington, New York: Robert Krieger Publishing Company. p. 57.
Wilson matrix is the following matrix having integers as elements:[1][2][3][4][5]
This is the coefficient matrix of the following system of linear equations considered in a paper by J. Morris published in 1946:[6]
Morris ascribes the source of the set of equations to one T. S. Wilson but no details about Wilson have been provided. The particular system of equations was used by Morris to illustrate the concept of ill-conditioned system of equations. The matrix has been used as an example and for test purposes in many research papers and books over the years. John Todd has referred to as “the notorious matrix W of T. S. Wilson”.[1]
has the factorisation with as the integer matrix[7].
Research problems spawned by Wilson matrix
A consideration of the condition number of the Wilson matrix has spawned several interesting research problems relating to condition numbers of matrices in certain special classes of matrices having some or all the special features of the Wilson matrix. In particular, the following special classes of matrices have been studied:[1]
the set of nonsingular, symmetric matrices with integer entries between 1 and 10.
the set of positive definite, symmetric matrices with integer entries between 1 and 10.
An exhaustive computation of the condition numbers of the matrices in the above sets has yielded the following results:
Among the elements of , the maximum condition number is and this maximum is attained by the matrix .
Among the elements of , the maximum condition number is and this maximum is attained by the matrix .
^Cleve Moler.
"Reviving Wilson's Matrix". Cleve’s Corner: Cleve Moler on Mathematics and Computing. MathWorks. Retrieved 24 May 2022.
^Carl Erik Froberg (1969). Introduction to Numerical Analysis (2 ed.). Reading, Mass.: Addison-Wesley.
^Robert T Gregory and David L Karney (1978). A Collection of Matrices for Testing Computational Algorithms. Huntington, New York: Robert Krieger Publishing Company. p. 57.