LAWSON - Least Squares Routines

LAWSON is a set of routines for solving least squares problems. The main purpose is consider an overdetermined M by N linear system A*X=B, and find a least squares solution X. This solution X has the property that it minimizes the L2 norm (square root of the sum of the squares) of the residual R=A*X-B.

Reference:

Charles Lawson and Richard Hanson,
Solving Least Squares Problems,
Prentice-Hall, 1974,
Revised edition, SIAM, 1995.

Files you may copy include:

• lawson.f90, the source code.
• lawson_prb.f90, a sample problem.
• lawson_prb.out, sample problem output.

The list of routines includes:

• BNDACC accumulates information for a banded least squares problem.
• BNDSOL solves a banded least squares problem accumulated by BNDACC.
• D_SWAP swaps two double precision values.
• DIFF is used in tests that depend on machine precision.
• G1 computes an orthogonal rotation matrix.
• G2 applies a rotation matrix to a vector (X,Y).
• GEN generates numbers for construction of test cases.
• H12 constructs or applies a Householder transformation.
• HFTI: Householder forward triangulation with column interchanges.
• LDP implements least distance programming
• MFEOUT labeled matrix output for use with singular value analysis.
• NNLS implements the nonnegative least squares algorithm.
• QRBD uses the QR algorithm for the singular values of a bidiagonal matrix.
• SVA carries out a singular value analysis.
• SVDRS: singular value decomposition also treating right side vector.

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