Campus Livre
lsqminnorm
Minimum-norm least-squares solution of a linear system.
Category: Mathematics > Linear Algebra
Syntax
x = lsqminnorm(A, b)Returns the x of smallest 2-norm among those minimizing norm(A*x - b).
Description
If A is rank deficient or has more columns than rows, infinitely many vectors give the same smallest residual. lsqminnorm picks the shortest one, the same answer as pinv(A)*b, found with a complete orthogonal decomposition instead of an explicit pseudoinverse.
Input arguments
A- Coefficient matrix of any shape or rank.
b- Right-hand side with
size(A,1)rows.
Output arguments
x- The minimum-norm least-squares solution.
Example
Rank-deficient and underdetermined systems
lsqminnorm([1 1; 1 1], [2; 2])
lsqminnorm([1 2 3], 6)Output
ans = 2×1
1.0000
1.0000
ans = 3×1
0.4286
0.8571
1.2857