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

svd.sm (59.92 KiB) downloaded 545 time(s).
svd.pdf (142.85 KiB) downloaded 362 time(s).

Best regards.
Alvaro.

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

svd_nr.pdf (122.43 KiB) downloaded 339 time(s).
svd_nr.sm (95.26 KiB) downloaded 502 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 533 time(s).
Maths SVD.sm (228.82 KiB) downloaded 530 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 564 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91.35 KiB) downloaded 493 time(s).
pinv.pdf (168.98 KiB) downloaded 295 time(s).

Best regards.
Alvaro.

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

pinv_svd.sm (161.03 KiB) downloaded 505 time(s).
pinv_svd.pdf (153.64 KiB) downloaded 340 time(s).

Best regards.
Alvaro.