Hi. Very short code. Singular Value Decomposition using QR decomposition.

svd.sm (59.92 KiB) downloaded 793 time(s).
svd.pdf (142.85 KiB) downloaded 450 time(s).

Best regards.
Alvaro.

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

svd_nr.pdf (122.43 KiB) downloaded 414 time(s).
svd_nr.sm (95.26 KiB) downloaded 764 time(s).

Best regards.
Alvaro.

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Thanks Alvaro ... OK all red SS 6179
I have no applications for the rectangular matrix.
Ultimately, all that stuff aims at solving singular square matrix,
2 examples Chemical Balance all done well.
Smath SVD can be used as well to sanity Greville.
Both documents take no time calculation.

Maths Pseudo Greville.sm (87.79 KiB) downloaded 787 time(s).
Maths SVD.sm (228.82 KiB) downloaded 780 time(s).

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Complete sanity vs Smath built-in SVD ... hyper fast.
Thanks Alvaro for sharing your great programming skill.

Maths svd.nr.sm (94.98 KiB) downloaded 823 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91.35 KiB) downloaded 743 time(s).
pinv.pdf (168.98 KiB) downloaded 388 time(s).

Best regards.
Alvaro.

Pseudo inverse, based in the previous (improved) SVD.

pinv_svd.sm (161.03 KiB) downloaded 754 time(s).
pinv_svd.pdf (153.64 KiB) downloaded 418 time(s).

Best regards.
Alvaro.